Solenoid cassette pump with servo controlled volume detection

ABSTRACT

Servo controlled solenoids provide actuation of a pump piston and valves, and electronic LC resonance measurements to determine liquid volume and gas bubble volume. Third order nonlinear servo control is split into nested control loops: a fast nonlinear first-order inner loop causing flux to track a target by varying a voltage output, and a slower almost linear second-order outer loop causing magnetic gap to track a target by controlling the flux target or the inner loop. The inner loop uses efficient switching regulation, preferably based on controlled feedback instabilities, to control voltage output. The outer loop achieves damping and accurate convergence using proportional, time-integral, and time-derivative gain terms. The time-integral feedback may be based on measured and target solenoid drive currents, adjusting the magnetic gap for force balance at the target current.

This Application is a divisional of application Ser. No. 08/882,945filed Jun. 26, 1997, now U.S. Pat. No. 6,208,497.

BACKGROUND

1. Field of the Invention

The present invention relates to systems and methods for controlling themovement of mechanical devices. More particularly, the present inventionrelates to the servo control of electromagnetic devices. Still moreparticularly, the present invention relates to the servo control ofsolenoids using the measurement of position and the approximation ofposition of the solenoid's armature to regulate movement of thatarmature. The present invention may be used in a variety of areas wherelifting and/or propulsion is desired with minimum energy consumption.

2. Description of the Prior Art

A solenoid is a linear motor, inherently capable of efficient conversionof electrical to mechanical energy. In rotary motors, experience teachesthat large size flavors efficiency, and for a given size motor, thehighest efficiency is obtainer when there are very close clearancesbetween stator and rotor parts and when operation is at high RPMs.Electrically speaking, a high frequency of magnetic reversals translatesinto a high rate of transfer of electromagnetic power. At lowfrequencies, resistive power losses wipe out efficiencies, while atconstant magnitudes of peak magnetic flux, higher frequency translatesinto higher power transfer without significant increase in I²R resistivepower loss. To avoid the eddy current losses associated with highfrequency magnetic fields, rotary motors employ laminations in magneticsteels, or high-resistivity ferrite parts. Steels have a large advantageover ferrites at moderately low frequencies (particularly below 1 KHz)in their ability to handle flux densities up to about 2 Teslas, comparedto ferrites at up to about 0.5 Teslas. The 4-to-1 advantage in fluxdensity translates into a 16-to-1 advantage in energy density andmagnetic force. Translating the rotary motor rules into the realm ofsolenoids, one can expect that efficient operation is fast operation. Afast solenoid must have a low shuttle mass, or alternatively, shuttleinertia may be cancelled by resonating its mass with a spring at thedesign operating frequency (as is done, e.g., in tuned magneticvibrators for aquarium diaphragm pumps and barber clippers). As thecounterpart of close clearances in rotary motors, solenoids operateefficiently at very short operating strokes, relying on high force andhigh frequency of operation to raise the power/weight ratio. Shortstrokes are effective only if, at the end of a power stroke, the entiremagnetic circuit closes with minimal air gaps—a matter of efficientdesign. For a solenoid shuttle in non-resonant operation, a short stroketranslates into a short stroke time, amounting to operation at highfrequency and a high rate of change of magnetic flux, “Φ,” as themagnetic gap closes. A high rate of change of flux, i.e., a large“dΦ/dt,” translates into a high induced magnetic voltage in relation toresistive voltage. Induced voltage represents conversion betweenelectrical and mechanical energy, while resistive voltage representsenergy loss, so a large “dΦ/dt” translates into high efficiency.

There are and will always be solenoids designed for utilitarian binarycontrol operations, e.g., unlocking the downstairs front door: contextswhere power efficiency is of minor importance and stroke length is amatter of feasibility and convenience, rather than a matter of efficientmotor design. Magnetic steel solenoid parts are typically solid ratherthan laminated, because eddy current losses in dynamic operation are nota design consideration. Moving from the context of infrequent operationof a door latch to the very frequent operation or a print wire driver ina dot matrix print head, repetitive impact and consequent work hardeningof the magnetic steel in a solenoid becomes a serious consideration.Magnetic materials for solenoids should ideally exhibit a low coerciveforce, i.e. a low inherent resistance to change in magnetic flux. Inmagnetic steels, low coercive force correlates with a large crystallinestructure, attained through high temperature annealing to allow growthof large crystals. Annealed steels are mechanically soft and ductile,and their low-coercive-force property is described as magnetically soft.Repetitive stress and shock break up large crystals in steel, yielding afiner grain structure that is mechanically work-hardened andmagnetically harder. Permanent magnets are optimized for high coerciveforce, or high magnetic hardness: the ability to retain magnetizationagainst external influences. In solenoids, the mechanical work hardeningof the steel takes place in a strong magnetizing field, leavingpermanent magnetism in the solenoid circuit. The result is to cause thesolenoid to stick in its closed position after external current isremoved. This is a failure mode for print wire solenoids. A standardapproach to keep solenoid parts from sticking is to cushion the landingat full closure, leaving an unclosed magnetic gap, typically through thethickness of the cushion material. This residual gap generatesresistance to residual flux after power removal, reducing the tendencyof the shuttle to stick closed. Residual magnetic gaps compromiseefficiency in two ways: because the most efficient part of the magneticstroke is approaching full gap closure, where the ratio of force toelectric power dissipation is high, and because currents for maintainingextended closure must be made substantially higher to overcome themagnetic resistance of gaps.

Prior art techniques for servo control of solenoid motion and, moregenerally, magnetic actuation, are summarized well in the introductorysection of U.S. Pat. No. 5,467,244, issued to Jayawant et al: “Therelative position of the object is the separation or gap between thecontrol electromagnet and the object being controlled and in prior artsystems is monitored by a transducer forming part of the control signalgenerator for the feedback loop. Such transducers have included deviceswhich are photocells (detecting the interruption of a light beam bymovement of the object); magnetic (comprising a gap flux densitymeasurement, e.g. Hall plate); inductive (e.g. employing two coils in aMaxwell bridge which is in balance when the inductance of the coils isequal); I/B detectors (in which the ratio of the electromagnet coilcurrent and magnetic flux is determined to provide a measure of the gapbetween electromagnet and object; for small disturbances the divisionmay be replaced by a subtraction); and capacitative (employing anoscillator circuit whose output frequency varies with suspension gap).”Dick (U.S. Pat. No. 3,671,814) teaches magnetic sensing with a Hallsensor. In the succeeding description of “Apparatus for theElectromagnetic Control of the Suspension of an Object” Jayawant et alderive, from a generalized nonlinear electromagnetic model, a linearizedsmall perturbation model for use in magnetic suspension of an object inthe vicinity of a fixed target position. Specifically, they make use ofwhat they call “I/B detectors” (see above quote) wherein the ratio ofcurrent “I” divided by magnetic field strength “B” provides anapproximately linear measure of the magnetic gap. In text to follow, theratio “I/Φ” will be used in preference to “I/B” since inductive voltagemeasurements lead to a determination of the total flux “Φ” rather than alocal flux density “B.” Specifically, as noted by Jayawant et al, thetime derivative “n·dΦ/dt” equals the voltage electromagnetically inducedin a winding of n turns linked by the magnetic flux “Φ.” Thus, timeintegration of the voltage induced in a coil yields a measure of thevariation in “Φ” and additional direct measurement or indirect inferenceof “I” leads to a determination of the ratio “I/Φ” used to close theservo loop. Where electrical frequency is substantially higher than thefrequency associated with solenoid mechanical motion, the ratio “I/Φ” isalso the ratio of the time derivatives “(dI/dt)/(dΦ/dt),” so that ameasurement of the high frequency change in current slope “dI/dt,”divided by the corresponding measured change in induced voltage across nwindings, “V=n·dΦ/dt,” again leads to a measure of position. Onerecognizes, in this latter ratio measurement, a measure of theinductance of a solenoid. It is well known that inductance can bemeasured by determining the natural frequency of an LC resonator havinga known capacitance “C,” a technique identified in the final part of thequotation from Jayawant et al, above. By either ratio technique, i.e.involving either a time integral of induced voltage or a time derivativeor current, one determines position without the use of sensors apartfrom means to extract measures or current and induced voltage from thecoil or coils employed as part of the actuation device. While theserelationships are needed building blocks in the conception of theinstant invention, they are not an adequate basis for a servo systemgenerating large mechanical motions and correspondingly large changes insolenoid inductance. First, there are limitations to the linearizedsmall-perturbation models taught by Jayawant et al for controlling largesolenoid motions. Second, dynamic stability problems would remain evenwith a more complicated and costly servo implementation using nonlinearcircuit models, e.g., computing position as the ratio of current/fluxand force as the square of flux, instead of Jayawant's tangential linearapproximations of the ratio and square law relations. Where solenoidcontrol is based on driving a winding with a voltage V in order tocontrol a position X, the system to be controlled is fundamentallythird-order, involving a nonlinear first order system to get fromvoltage to change in magnetic force (since voltage controls the firstderivative of current in an inductive solenoid, and current changegenerates force change without significant delay), coupled to a secondorder system to make the two hops force to change in velocity and fromvelocity to change in position. It is understood that servo control overa third order system is prone to instability since phase shifts aroundthe control loop, tending toward 270 degrees at high frequencies,readily exceed 180 degrees over the bandwidth for which control isdesired. Phase-lead compensation as taught by Jayawant et al adds 90degrees of phase margin, bringing at best marginal stability to anefficient electromechanical system. If electromagnetic efficiency isvery low, so that resistance R dominates over inductive impedance ωL upto the servo control bandwidth of ω, then the third order nature of thesystem is not manifest where gain exceeds unity, and phase-leadcompensation provides an ample stability margin. An example of such alow-efficiency system is found in Applicant's “BearinglessUltrasound-Sweep Rotor” system (U.S. Pat. No. 5,635,784), where acombination of extreme miniaturization and lack of a soft ferromagneticcore places the transition from resistive to inductive behavior wellinto the kilohertz range. For the efficient actuation systems taught inthe instant invention, the transition from resistive to inductiveimpedance can fall below 100 Hz. “Tight” servo control implies arelatively high loop gain over the bandwidth of significant mechanicalresponse, implying a loop gain-bandwidth product well in excess of thebandwidth of significant mechanical response. A combination of highefficiency and tight control spell problems for loop stability, for evenwith single-pole phase lead compensation, minor resonances, e.g., frommechanical flexure, can throw the servo system into oscillation.

While Jayawant et al describe closed-loop servo control techniquesapplicable where perturbations in position from a fixed target positionare small, Wieloch (U.S. Pat. No. 5,406,440) describes an open-loopcontrol technique for reducing impact and mechanical bounce in solenoidsused in electrical contactors. Prior art actuation had consisted ofinstantaneously applying to the solenoid winding the full voltage neededto close the contacts under all operating conditions, taking intoaccount manufacturing variations in the spring preload holding thecontacts open. The fixed actuation voltage was usually well in excess ofthe minimum requirement, and the result was actuation with excessiveforce and resulting severe contact bounce. Wieloch teaches to ramp thesolenoid current up slowly so that when the magnetic force is justsufficient to overcome spring preload force and initiate motion, therewill be little additional increase in average actuation voltage beforethe solenoid stroke is complete. Efficient current ramping isaccomplished via a switching regulator, which applies a steadilyincreasing voltage duty cycle to the solenoid winding while windingcurrent recirculates through a diode during intervals between drivingvoltage pulses. At a sufficiently high switching frequency, theinductance of the solenoid effectively smoothes the current waveforminto a ramp. Similar switching regulation is found in preferredembodiments of the instant invention, but with greater control in orderto overcome limitations in Wieloch's soft landing design. When asolenoid begins to close, the resulting “back EMF” due to armaturemotion tends to reduce electric current, in relation to gap, to maintaina constant magnetic flux, with the result that increases in force withgap closure are only moderate. (The simplified model of Jayawant et al,equation 9, implies no change at all for force as a function of gapclosure at constant magnetic flux. In the specification below, Eq. 42corresponds to equation 9 except for the slope function “dx_(eff)/dx,”which Jayawant takes to be unity and which departs significantly fromunity for moderate to large magnetic gaps, as indicated, e.g., in theapproximate formulation of Eq. 20 of the following specification.) If aconstant average voltage is applied to the winding (e.g., via constantduty cycle voltage switching at high frequency) and current begins todecrease with gap closure, then the current-limiting effect ofresistance is reduced as current is reduced, so that the magnetic fluxbegins to rise. This can lead to an acceleration of a solenoid armaturetoward impact at full closure, depending on inductive time constants,mechanical inertia, and spring rate. Even under conditions wheresufficiently soft landing is achieved, it is at the cost of asubstantial excess energy consumption to generate a long ramp of pulseduty cycle and current, only the middle portion of which causesactuation. Adaptive adjustment of a pulse width or a pulse duty cycleduring solenoid closure will be shown (below) to achieve soft landingunder variable conditions with nearly the minimum net expenditure ofelectrical energy dictated by the given operating conditions.

Hurley et al (U.S. Pat. No. 5,546,268) teach an adaptive control devicethat regulates electric current to follow a predetermined function ofthe measured solenoid gap, in order to achieve a predetermined pullcurve of the electromagnet. Though such a system responds to some of thelimitations of Wieloch, it is not readily adaptable to an actuationsystem that must respond to changing conditions of starting position andthe load force curve while achieving quiet, impact-free, efficientoperation.

Both for controllability and energy efficiency, some solenoids have beendesigned with a region of operation in which stator and armaturecomponents have closely spaced parallel surfaces and the armature movesin-plane through a region of changing overlap, yielding a region ofrelatively constant actuation force at constant current. Eilertsen (U.S.Pat. No. 4,578,604) teaches such a geometry in a dual-coil device forlinear mid-range actuation and a strong holding force at either end ofthe actuation stroke. Rotary actuation designs accomplish similarlinearity properties using rotary overlap of parallel magnetic plates.The touchdown region where magnetic parts close in contact is commonlyavoided in servo control contexts. Magnetic characteristics in thisregion have presumably been considered too nonlinear for practicalcontrol. In particular, the region of operation approaching full closureand contact of mating magnetic surfaces presents a very steeply changinginductance and correspondingly steep change in the sensitivity of forceto change in coil current. For a solenoid operated below coresaturation, the variation in magnetic force “F” with coil current “I”and magnetic gap “x” is described approximately by the proportionality“F∝(I/z)².” When the gap in a solenoid reaches mechanical closure, the“x” denominator in this proportionality goes nearly to zero, implying anearly singular relationship between the control variables and theresulting magnetic force. Interpreting published families of staticforce/stroke/voltage curves exhibiting approximately thisproportionality equation, the engineer is likely to conclude that aposition servo control loop becomes unmanageably nonlinear over wideactuation ranges or on approach to full magnetic closure of thesolenoid. As evidence of the prevalence of this assumption, FIG. 2 ofthe recent Jayawant patent (U.S. Pat. No. 5,467,244) illustrates theproportionality “F∝(1/x)²” for magnetic force as a function of distanceand indicates a small region, designated by the symbol “Δ,” over whichthe curve is comparatively linear and amenable to linear controltechniques, which are subsequently disclosed. What has gone unrecognizedis that a reformulation of the control problem leads to division of thesystem into two well-behaved, coupled subsystems: a fast first-ordercontroller using voltage to control magnetic force, and a slowersecond-order position servo using the force-control servo. The majorsystem nonlinearities are confined to the robust first-order controllersubsystem. Thus, from a control standpoint, there remains no advantageto magnetic geometries that linearize the relationship of force toarmature motion, whereas one can now capitalize on the advantages ofmechanical simplicity and economy in solenoid geometries that involvethe mating of flat surfaces. Such simple geometries are found in thepatent literature going back many years, e.g., to Kussy (U.S. Pat. No.3,324,356). Such geometries give a strong nonlinearity of force with gapat constant current, which needs to be countered by appropriatecontroller design if the mechanical economies of flat geometries are tobe realized.

Holding currents or drive voltages for solenoids are commonly set wellbelow the peak currents or voltages needed to get a solenoid movingtoward closure. Both drive and holding signal levels must, in open loopsystems, be set high enough to insure closure followed by holding underall conditions, including variability in manufacture from unit to unit,including variability of power supply source (e.g., utility linevoltage), and including variability in the mechanical load. Closed loopsolenoid control offers a way to reduce both drive and holding signalsto minimum practical levels. Yet problems with stability andnonlinearity inherent to magnetically soft ferromagnetic-core solenoidshave impeded the development of servo solenoids, and therefore haveprevented the potential efficiency advantages just described.

Solenoids have the potential for operating characteristics nowassociated with efficient motors: quiet impact-free operation, veryfrequent or continuous motion, and high efficiency at convertingelectrical energy to mechanical work. Reciprocating power fromelectricity is traditionally derived from a rotating motor and a cam orcrank shaft, yet solenoids have been demonstrated, in the instantinvention, to deliver reciprocating power at high efficiency, providedthat the solenoid is designed to operate fast, in order to generaterapid changes of magnetic flux in its windings. In many reciprocatingpower applications, a solenoid with sophisticated control can offergreater simplicity and substantially tighter control than is achievedwith a rotary motor and rotary-to-reciprocating motion conversiondevice. In the realm of control and sensing of external processes via asolenoid, the invention to be disclosed below can be configured tooperate as a controller of position and simultaneous sensor of force, oras a controller of force and simultaneous sensor of position, or in anintermediate mode as a source of mechanical actuation with electricallycontrolled mechanical impedance characteristics, especially ofrestoration and damping. With rotary motors, such control has involvedthe use, e.g., of stepper motors used in conjunction with torque orforce transducers, or of non-stepper motors used in conjunction withrotary position encoders and possibly torque or force transducers. Thefollowing specification will show a solenoid operated as the linearmotor to drive a high-efficiency reciprocating pump, while twoadditional solenoids control the pump's inlet and outlet valves. Allthree solenoids operate silently and efficiently under servo control.This new system goes beyond objectives described and claimed inApplicant's U.S. Pat. No. 5,624,409, “Variable-Pulse Dynamic Fluid FlowController,” a system using valve solenoid actuators that aremechanically similar to the ones described below and that achievevolumetric flow regulation from a pressurized fluid source over a verywide dynamic range of pulse volumes and rates. The system describedbelow replaces the volume measurement device of Applicant's earlierinvention with a solenoid that provides active pumping actuation inaddition to fluid volume measurement, inferred from the position of thesolenoid pump actuator, where that position is determined frommeasurement of the resonant frequency of the solenoid drive winding witha capacitor.

OBJECTS OF THE INVENTION

An object of the invention is control of the powered closure of asolenoid to eliminate closure impact and associated noise, efficiencyloss, and progressive damage, including damage to the properties of themagnetic materials. Related objects are to eliminate closure impactthrough two strategies: a low-cost strategy called “launch control;” anda feedback strategy called “servo control.” A further object is toemploy servo control for dynamically maintaining a solenoid position ina hovering or levitating mode. A still further object is to employ servocontrol for smooth opening of a solenoid.

Within “launch control” an object is to infer, from current signalsand/or induced voltage signals, a parameter to be compared to athreshold function for determining, dynamically, a time to terminate alaunch pulse, such that the solenoid gap closes approximately to atarget value short of full closure and short of impact.

Within mechanical “servo control,” common terminology describes a senseparameter; indicating mechanical response of a servo system; a targetparameter to be subtracted from the sense parameter and resulting in anerror parameter; PID gain parameters describing three aspects offeedback amplification of the error parameter, namely: Proportionalfeedback; Integral feedback; and Derivative feedback, and a driveparameter arising from the summation of the P, I, and D feedbackcomponents and that determines the actuation output causing thecontrolled mechanical response. A servo control loop is characterized bya settling time constant, which may be defined by the shortest timeinterval beyond which an error parameter continues to be reduced by atleast a specified ratio below an initial error defined at the start ofthe time interval. The settling time constant is generally minimized byan optimum combination of proportional and derivative feedback gains.Increasing of the integral feedback gain generally improves long termerror reduction while increasing the settling time constant, thusdegrading short term settling and, for excessive integral feedback gain,causing instability and oscillation of the servo system.

Within this descriptive framework, in the context of sense parametersfor servo control, and where the magnetic gap of the solenoid isidentified in the instant invention as the parameter to be sensed andcontrolled, an object is to employ a measure of solenoid current as asense parameter of the servo loop. It is a related object to exploit thedirect electromagnetic interaction between magnetic gap and solenoidcurrent that inclines solenoid current to vary, in the short term andneglecting external influences, in approximate proportion to magneticgap. It is a further related object to exploit the relationshipdemanding that, when a servo control loop causes electromagnetic forceto balance against a mechanical load force, the result is to establish asolenoid current that necessarily varies in approximate proportion tomagnetic gap. Given that, within the context of ongoing servo control,solenoid current is caused to vary in approximate proportion to magneticgap, both in the short term due to the physics of the electromagneticinteraction, and in a longer term due to the force-balancing propertiesof the servo loop, it is an object to employ solenoid current as a senseparameter indicative of solenoid magnetic gap, including for servocontrol.

In an alternative embodiment of servo control employing an alternativesense parameter, the actuation output of the servo system is the outputof a switching amplifier, which causes the voltage differential across asolenoid coil to switch between two known values with a controlled dutycycle, resulting first in duty cycle control over the coil current asaveraged over one or more switching cycles, and resulting second in ameasured AC fluctuation of the time derivative of current in thesolenoid coil. That AC fluctuation varies monotonically and consistentlywith the magnetic gap of the solenoid, providing a repeatable measure ofthat gap. An object, therefore, in a solenoid system driven by aswitching amplifier with duty cycle control, is to employ the measuredAC fluctuation in current slope as a sense parameter of the servocontroller.

Total magnetic flux through the solenoid and coils, designated Φ, is avaluable controller parameter related to magnetic force and todetermination of magnetic gap, i.e. position. An object of the inventionis to determine variation in magnetic flux in a controller byintegration of the voltage induced in a coil linked by the solenoidflux. A further related object is to determine absolute flux byinitializing the flux integral to zero for an open magnetic gap and whensolenoid current is zero. A further related object is to determineinduced voltage in the solenoid drive winding by subtracting an estimateof resistive coil voltage from the total voltage across the coil. Astill further related object is to measure induced voltage in anauxiliary sense winding, coaxial with and electrically separate from thedrive winding.

In the context of related drive parameters, sense parameters, and targetparameters for servo control, an object is to split a solenoid controlservo system functionally into coupled inner and outer loops withdistinct drive, sense, and target parameters, and such that the innerloop has a substantially shorter settling time constant than the outerloop. A related object is to establish an outer control loop for whichthe sense parameter is a measure of position and the drive parameter isa signal related to force. The sensed measure of position may be asolenoid current, or a measured AC variation in a solenoid currentslope, or an auxiliary measurement of mechanical position, e.g., via ahall effect sensor and permanent magnet or an optical sensor and a lightsource. A further related object is to establish an inner control loopfor which the sense parameter is a measure of variation in magneticflux, and for which the drive parameter of the outer loop defines atleast an additive component of the target parameter being compared withthe sensed measure of magnetic flux, and for which the drive parameteris a coil-drive voltage. Note that this drive voltage is the actuationoutput ultimately controlling mechanical motion in the solenoid. A stillfurther related object is to establish an efficient voltage switchingoscillation in an amplifier driving a solenoid coil, and to cause theduty cycle of that switching oscillation to vary such that theshort-term-average voltage driving the coil is the voltage driveparameter of the inner loop. As a way of simplifying the electronicdesign of the servo system, an objected related to the establishment ofa switching oscillation with a controlled duty cycle is to design acontroller loop with an intentional short-term instability that givesrise to switching oscillations having the desired characteristics.

We recognize that, over periods substantially longer than the timeconstant defined by the solenoid inductance/resistance ratio L/R, theaverage voltage applied to a solenoid coil determines the coil current,while inductive effects are “forgotten.” We further recognize that theIntegral component of PID feedback control is sensitive only tocomparatively persistent or long term trends in the input error signal.From these recognitions, it follows that it is possible to substitutevoltage or duty cycle for sensed current in the integral component of aPID feedback controller, with similar long-term results, even thoughsettling characteristics will differ. An object is therefore to designcontrollers based on integral feedback whose sense variable may be drivecurrent or drive voltage or drive duty cycle. For any of these choicesof sense variable, the equilibrium magnetic gap established by servocontrol is dependent on a combination of mechanical load force and thecontroller target for the sense variable in the integral loop, i.e. thetarget for current or voltage or duty cycle. In any of these cases, anobject of the invention is a controlled solenoid able to pull to nearclosure and hold there with a practical minimum of electric power. Thiscan be accomplished by setting the bias for zero rate-of-integration ata signal level that is determined in advance to be sufficient to holdthe solenoid at a finite gap.

The solenoid of the instant invention can include permanent magnetmaterial, so incorporated that a needed range for holding force isobtained, at zero drive coil current, over a corresponding useful rangeof the solenoid gap. In such a permanent magnet-incorporatingembodiment, an object is to set the bias for zero rate-of-integration ator near zero drive coil current, so that except for power transients tocompensate for perturbations from equilibrium, the control systemachieves solenoid holding with vanishingly small drive power. With orwithout the inclusion of a permanent magnet, the moving element of thesolenoid may be free-floating, in which case an object of the inventionis to achieve stable electromagnetic levitation of a free-floatingmagnetic element. A further related object is to achieve levitation witha minimum of actuation power.

In controlling substantial currents to a solenoid winding, there aredifficulties and disadvantages to incorporation of a current-senseresistor and associated differential amplification, including thedifficulty of having to sense across a resistor whose common modevoltage swing travels outside the power supply range, and including thedisadvantage of added power dissipation in the current-sense resistor.The differential voltage output provided by an isolated flux-sensewinding, wound coaxial with the power drive winding, carries all theinformation necessary for the dynamic determination of both current “I”and magnetic flux “Φ” when such a sense winding is used in conjunctionwith a switching mode drive. It is therefore an object of the inventionto employ a sense winding for the determination of both coil current andmagnetic flux in a switching mode solenoid controller.

From sense coil information, one can derive either the “integral ratio”designated “I/Φ” or the “derivative ratio” designated “(dI/dt)/(dΦ/dt),”or the “derivative difference ratio” designated “Δ(dI/dt)/Δ(dΦ/dt),” anyof these three ratios being a measure effective magnetic gap andtherefore a measure of position, for servo control. The integral ratiodepends on a determination of absolute flux, as mentioned above and asfeasible when the flux integral, as defined by integration of allinduced voltage, can be initialized under known zero-flux conditions,e.g. zero for an open magnetic gap and a winding current of zero. Afurther limitation to absolute flux determination is integration drift,which introduces errors in an absolute flux determination if too muchtime elapses after initialization. Another disadvantage of the integralratio is the requirement for division. In some embodiments of theinstant invention, effective especially for servo control as themagnetic gap approaches close to zero and magnetic flux approaches aconstant value that generates a force approaching balance with aconstant load force, the denominator of the integral ratio isapproximated as a constant, resulting in the use of current “I” as asense parameter. This approximation fails, leading to all unstablecontrol loop, under conditions of excessive loop gain or for excessivelylarge magnetic gaps. A more robust controller therefore avoids theconstant denominator approximation of the integral ratio and eithercomputes the true integral ratio, or makes use of the derivativedifference ratio, or makes use of a direct measure of position via anauxiliary sensor. In a switching regulator context, the denominator ofthe derivative difference ratio, namely Δ(dΦ/dt), is equal to 1/n timesthe peak-to-peak voltage swing of the switching amplifier output, where“n” is the number of turns in the drive winding. Thus, for a constantdrive voltage swing, the denominator of the derivative difference ratiois constant, and the numerator varies in direct proportion to effectivemagnetic gap. An object, therefore, is to achieve a more robustcontroller, less prone to instability, by using an accurate measure ofeither the effective magnetic gap or the true geometric position as thesense parameter of the outer control loop. A related object is to usethe ratio of current divided by flux, I/Φ, as the sense parameter forthe outer control loop. An alternative related object in a voltageswitching servo is to use the peak-to-peak current slope amplitude,“Δ(dI/dt),” or an approximate measure of this current slope amplitude,as the sense parameter of the outer control loop. For operation of asolenoid approaching full magnetic closure, the sawtooth currentwaveform resulting from a switching voltage drive becomes veryunsymmetric, with short steep rises in current (when a drive voltage isapplied) followed by much more gradual decreases in current wherecurrent is impeded by only a small resistive voltage and a small dropacross a diode or on-state transistor. In this situation, thepeak-to-peak current slope amplitude is well approximated by thepositive-going current slope designated “İ>0” where the much smallernegative current slope going into the difference “Δ(dI/dt)” isneglected.

In controller contexts where sensing and servo control of truemechanical solenoid position is required over extended periods, wherethe time-integral determination of total magnetic flux will be prone todrift, effective magnetic gap “X” is determined without drift in aswitching regulator context by the relation “X=K·Δ(dI/dt)” as describedabove, and magnetic force “F” is well approximated in relation tocurrent “I” by the equation “F=K2·(I/X)²” An object of the invention istherefore to construct a servo controller driving a solenoid drivewinding with a switching amplifier and utilizing the oscillatoryamplitude of current slope, or the positive-going current slope, as adrift-free measure of magnetic gap X. A related object is to use thesquare of the ratio of current to magnetic gap, (I/X)², as a measure ofelectromagnetic force. In an oscillatory feedback loop, only the sign ofan inequality involving nonlinear variables need be determined in orderto define the switching amplifier output as high or low at a giveninstant. Such an inequality involving ratios of variables and powers ofvariables is readily computed in an analog controller as an inequalityinvolving logarithms of electronic variables, those logarithms arisingfrom the inherent logarithmic voltage/current characteristics ofsemiconductor diodes or bipolar transistors. An object of the inventionis therefore to design an oscillating servo controller circuit withoutput voltage switching based on the sign of an inequality involvinglogarithmic signals. A related object is to define a position senseparameter as an oscillatory amplitude of current slope. A furtherrelated object is to define a magnetic force as the square or the ratioof solenoid current divided by a position sense parameter. A stillfurther related object is to employ a comparator circuit and logarithmictransistors to determine the sign of an inequality involving thelogarithm of an oscillatory amplitude of current slope and the logarithmof current.

In systems applications of a servo controlled solenoid, it is sometimesuseful to use the solenoid as a precision measurement device, whereposition of the solenoid armature correlates with a system parameter tobe determined, e.g., fluid volume. When a solenoid is designed for goodperformance in a servo system, e.g., by employing a powder metal orferrite core to avoid eddy currents that otherwise confuseelectromagnetic measurements, and/or by including a flux sense windingin addition to the drive winding, then the solenoid becomes more usefuland accurate as a position measurement device. As mentioned above,position, as related to effective magnetic gap, can be measured usingany of the three ratios of current over flux, namely the integral ratio,the derivative ratio, or the derivative difference ratio. Yet anotherway to measure effective magnetic gap and infer position is bymeasurement of the resonance frequency of a solenoid winding coupled toa capacitor. Since the solenoid is capable of exerting a selectable orvariable force while measuring position, it can therefore be used forthe quantitative measurement of mechanical compliance. In a fluid-movingsystem employing solenoid actuation, measurement of position can be usedto measure volume, and measurement of mechanical compliance can be usedto measure fluid volume compliance, e.g., as an indication andquantitative measure of bubbles present in a substantiallyincompressible liquid. An object of the invention is therefore to makedouble use of a solenoid as an actuator and as a position measurementsensor. A related object is to use a solenoid to measure mechanicalcompliance. A related object in a fluid moving system is to make doubleuse of a solenoid for pumping and fluid volume measurement. A furtherrelated object in a fluid moving system is to use a solenoid to measurefluid volume compliance, including as an indication and quantitativemeasure of bubbles in a liquid.

In an application of the invention for developing a sustained magneticclosure force for holding or magnetic bearing or magnetic levitationfunctions, an object is to combine permanent magnet materials with softmagnetic materials to generate a passive force bias, whereby thecontroller generates output drive currents that fluctuate about a zeroaverage to correct for deviations from an unstable equilibrium pointwhere steady magnetic force is derived entirely from the bias of thepermanent magnet material. A related object is adaptively to seek outthe levitating position for which the electric drive current required tohold velocity to zero is a zero drive current, and where non-zero drivecurrent signals are integrated to generate a cumulative bias correctionthat drives the system toward the balance position calling for zerodrive current.

In an application of the invention to magnetic levitation and propulsionof a monorail car, an object is to control multiple magnetic liftingmodules in a common mode for regulating height of levitation, in adifferential mode for regulating tilt, and in a variable-gain travelingwave mode for generating thrust through engagement of traveling magneticwaves with periodic ripples in a track. A related object for minimizinghysteresis and eddy current losses in a track is to generate liftingforces of magnetic attraction from magnetic fields directed mostlyvertically and laterally relative to a longitudinal direction of motion,thereby generating magnetic flux in the track that remains relativelyconstant during the period of passage of a levitating car. A relatedobject for minimizing lifting power is to combine permanent and softmagnetic materials for generating lift with a reduced or zero-averagecurrent to electromagnetic lifting modules.

SUMMARY OF THE INVENTION

The parameter X defined by X=I/Φ, for solenoid primary winding current Iand total flux Φ linking that winding, is called effective magnetic gapand varies approximately in proportion to the geometric gap of asolenoid with a flat-ended pole piece. This effective gap X is used invarious solenoid servo controller embodiments, having the-advantage ofderivation from coil measurements without recourse to auxiliary sensors(e.g., optical encoders or hall effect devices.) The induced voltage Viin a winding of n turns is given by Vi=n(dΦ/dt), so time integration ofinduced voltage yields a measure of variation in Φ. For controllersstarting with an open magnetic gap and zero solenoid current, theinitial flux is zero, so integration of Vi from a zero initial conditionat zero initial flux yields an absolute measure of Φ. Vi in turn can bemeasured as the voltage differential across a solenoid drive winding,subtracting out the resistive voltage component IR for current I andwinding resistance R. Alternatively, Vi can be measured directly from asense winding wound coaxial with the drive winding, without need tosubtract out a resistive voltage. Thus, effective gap X can bedetermined from a measurement of current and the integral ofmeasurements of induced voltage, starting from an initial condition ofzero. In the important situation where a solenoid is converging underservo control to rest at a near-zero value of gap X, where magneticforce is balancing a mechanical load that approaches a limiting force asgap X approaches its final, small value, then flux Φ, the primarydeterminant of magnetic force, must necessarily approach a constant Φ asgap X closes to its final value. Under these circumstances, a controllercan be based on the approximation that I/Φ≅I/Φ₀, so that thedetermination of flux and the division operation are both eliminated. Analternative approach to determination of effective gap X is based on ACinductance measurements, using the relation X=n/L for inductance L in nwindings. For precision measurements of X, appropriate for static orslowly changing X, a solenoid winding can be resonated against acapacitor C, measuring the resonant frequency, and solvingmathematically for X. Resonance determination methods include: “pinging”with a transient excitatory pulse and monitoring of the ringingfrequency; oscillation of a regenerative feedback loop involving the LCresonator; and phaselock loop techniques. For determination of X in aservo circuit where a switching amplifier drives the solenoid windingwith a variable duty cycle, the peak-to-peak switching drive voltage,ΔV, is related to the peak-to-peak change in current slope, Δ(dI/dt), byreciprocal inductance, which in turn is related to X. When ΔV is aconstant pulse amplitude, then Δ(dI/dt) varies in linear proportion toX. In the important limit where gap X is approaching smoothly to a smallfinal value, then the drive voltage pulses are becoming comparativelynarrow, resistive voltage drop in the drive coil is becoming a smallfraction of the on-state drive voltage, and the difference Δ(dI/dt) isapproximated by the value dI/dt sampled when the drive voltage is on andthe magnitude of I is increasing: a technique illustrated in FIG. 12 bythe parameter labeled “İ>0.”

A servo control loop for operation of a solenoid includes a relativelyslow outer loop for regulating magnetic force in order to control thesense parameter X, and a much faster inner loop to vary average outputvoltage in order to satisfy the force demand of the outer loop. Morespecifically, magnetic force varies approximately as the square ofmagnetic flux, i.e. Φ², more or less independent of gap X. For the smallfractional perturbations in total force that arise when a solenoid witha spring load converges to a target value of gap X, force is describedby a constant plus a linear term in flux Φ. Thus, the input senseparameter of the inner loop is X, and the output is Φ, which controlsforce. This output is the input target parameter of the inner loop,whose output is typically duty cycle from a switching amplifier. Dutycycle drives current, which controls Φ, the flux that is sensed at theinput of the inner loop and compared to the target flux dictated by theouter loop. Flux also controls the magnetic force that causes variationin acceleration of the position parameter X, closing the second-orderouter loop. X is compared to an externally-provided target, X₀, to yieldthe error signal of the outer control loop. Typically this error signalis processed by a linear transfer function whose output is characterizedby the three gain terms of traditional PID control: a Proportional, atime Integral term, and a time Derivative term. The weighted sum of theP, I, and D terms, plus a bias constant corresponding to an estimate ofΦ₀, the flux expected at final equilibrium, yields the target flux fromthe outer loop to the inner loop.

This hierarchy of interacting loops with different speeds splits aninherently difficult-to-control, nonlinear third order controller into asecond order linear controller (the outer loop) and a first ordernonlinear controller (the inner loop). The rate behavior of the innerloop is approximately linear, since flux Φ is controlled by averageoutput voltage V (averaged over variable-width pulses) and thecontrolling physical equation is V=n(dΦ/dt), a linear first orderequation. The nonlinearity resides in a variable offset or inhomogeneousterm, IR, the component of voltage necessary for current I to overcomeohmic resistance R and maintain the current required to produce flux Φ.This inhomogeneous term in the linear controller loop varies more orless in linear proportion to X for constant force, and nonlinearly withrespect to required variations in magnetic force. In effect, the innerfirst-order control loop must respond to a time-varying input target andto a nonlinear time-varying voltage offset in its output (due toresistive voltage drop) in order to drive its input error to zero.Hence, a difficult nonlinear third order controller problem is-segmentedfirst by speed, to solve a first order equation rapidly and reduce theremaining control problem from third to second order, and second byconfining nonlinearity to the simpler first-order loop, wherenonlinearity appears as an innocuous variable offset term.

Means for measuring or determining the position parameter X werediscussed above. Also mentioned was determination of flux Φ fromintegration of a measured induced voltage, either directly from a sensewinding or with correction for resistive voltage drop from a drivewinding. Where control of force is concerned, it is not necessary thatthe estimation of flux Φ be free from offset or drift with respect totime. The integral component of a PID control loop automaticallycorrects for offset and gradual drift in the estimation of flux. Thecontrol loop may also be designed so that the integration from inducedvoltage to flux, and from position error to the integral term of the PIDcontroller signal, takes place in the same integrator, whose output is asum of terms made immune to drift by the action of corrective feedbackthrough the entire servo loop. In controller configurations whereestimates of position X include linear terms in both current I and fluxΦ, the integral component of the PID loop may be based not on X, but ona correlate of X at equilibrium. For example, for a known range ofstatic weight and/or spring forces at a holding value of X near zero,i.e. hovering at a negligibly small gap after impact-free solenoidclosure, both the steady voltage and the steady current required to keepX in the required small range can be determined in advance. The integralcontrol loop uses as its input, therefore, not X, but the voltage orcurrent determined by the faster proportional and derivative componentsof the control loop. If the steady gap is “wrong” then the operatingcurrent and voltage will be off-target. Specifically, if the current andvoltage are too high, relative to the target, this indicates that themagnetic gap X is too large, causing an excessive current demand todrive magnetic flux across the gap. Thus, paradoxically, the integralcontroller must gradually demand still more current, to drive X to asmaller value, so that less current is demanded. The magnetic force atconstant current is destabilizing, with a smaller gap giving a greaterforce to close the gap more. The integral control loop is “unstable” or,specifically, regenerative, responding to an excess current with a rateof increase in current. The regenerative control loop interacts with thedestabilizing magnetic property of the gap to give a stable closed loopbehavior, as the product of two negative stabilities yields a positivestability.

A solenoid adapted for servo control based on sensed electromagneticparameters is also well adapted for use as a position sensor, based ondetermination of the reciprocal of inductance, a parameter that is awell-behaved monotonic indicator of solenoid gap. Position sensing isemployed in a pumping system for determination of pumped liquid volumeand for quantitative determination of air bubbles present in a pumpedliquid, as inferred from changes in solenoid position with changes inelectromagnetic force.

In steady lifting and levitation applications, permanent magnetmaterials are combined with soft magnetic materials to generate alifting bias force at zero cost in steady coil power. The principles ofservo control and efficient switching-regulator drive taught elsewherein this Specification are readily adapted to operation with a permanentfield bias and to stabilization of an otherwise inherently unstablepermanent-magnet suspension system. These principles are extended tolevitation and tilt control in a levitated monorail car, whosepropulsion is generated by a perturbation in the lifting magnets togenerate traveling waves of magnetic field strength that aresynchronized to the passage of ripples in the track.

In another application of the invention, where real-time closed-loopservo control is not required, knowledge of the known characteristics ofthe system is embodied in coefficients of a “launch control” apparatusand method, whose goal is to compute, in advance of launch, apre-programmed sequence of pulses predetermined starting times andwidths, designed to move the solenoid armature, or shuttle, quickly andwith a near-minimum of electrical energy consumption, from a startingposition to a target finishing position. In systems contemplated here,this pulse sequence begins (and possibly ends) with a single launchpulse of duration designed to bring the solenoid armature to a stop at atarget position. If that position is near magnetic closure but short offull closure and an impact click, and if the solenoid is to be heldclosed electromagnetically, then a pulse sequence follows to gently pullthe armature the remaining distance to fill gap closure, followed bypulse train at reduced duty cycle to maintain closure. In situationswhere the starting position is variable or otherwise unknown to thesystem software before launch time, then the initial position ismeasured either by electronically connecting a capacitor to a solenoidwinding and using one of the resonance methods described earlier in thissection, or by using a “probe pulse” from the solenoid driver to providedata adequate to compute a ratio of current/flux, “I/Φ).” The resonantfrequency or the current/flux ratio thus determined is used to computethe previously unknown initial position or, more to the point, theparameters necessary to define a launch pulse duration. If themechanical characteristics of the solenoid and load are well enoughknown in advance, then the pre-launch data alone is applied to anempirical formula describing the pulse width that will be required.There may be corrective adjustment for measured power supply voltage, aswell as for power supply impedance based on measurements from recentlaunches (which is a significant issue for operation from an unregulatedbattery supply whose voltage and impedance will change as the battery isprogressively discharged.)

If the unknown characteristics of the system include parameters that arenot readily determined in advance of a launch, e.g., when an unknowneffective preload force must be overcome to initiate motion of thesolenoid armature from its initial position, then the launch controlmethod includes an on-the-fly correction to the launch pulse duration.In a specific application of the launch controller to pumping with asolenoid-driven piston stroke, the effective preload force is affectedby an unknown fluid pressure. Since the pressure is isolated from thesolenoid by a valve (passive or active) that remains closed untilroughly the moment in launch when the solenoid armature starts to move,the solenoid controller can obtain no advance knowledge of the preloadforces that will affect launch. The effect of the preload force willfirst manifest itself to the system sensors as an advance or delay inprogress toward gap closure. This progress is most readily observed inthe waveform of current drawn by the solenoid during the launch pulse.Before the armature begins to move, the current waveform will describean exponential decay from zero upward toward a resistive upper limit ofcurrent. Acceleration of the armature toward closure will rapidlycurtail and reverse the upward trend in current. At any given instant,the value of current will be less than, equal to, or greater than apredetermined threshold function of time. When the sensed currentwaveform crosses the threshold function, the drive pulse is terminatedand the solenoid coasts to its target. The shape of the thresholdfunction is determined, in advance, to cause the desired outcome, whichis generally to have the solenoid armature come to a halt slightly shortof full closure and impact. When the armature is expected to havestopped, a pull-in pulse train may be applied to close the remaininggap, or valve closure may prevent the armature from falling back. Acomparable threshold function may be defined for another sensedparameter, e.g., the output voltage from a sense winding. Thesensitivity of the sense function to incipient armature motion may beenhanced by including time derivative terms of sensed current of inducedvoltage. In any case, a motion-sensitive sense parameter is compared toa threshold function of time, and the crossing of the parameter and thefunction causes launch pulse termination at a time predetermined to sendthe armature to the vicinity of a target.

Implementation of the invention summarized above relies on specificquantitative models of solenoid electromechanical dynamics. While partsof these models are to be found scattered among textbooks, the materialto follow pulls together the mathematical and formula relationshipsnecessary for the detailed implementation of the apparatus and methodstaught. Following a list of the drawings, we begin with fundamentalrelationships and move forward to applied formulas.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates parameter traces, against a time axis, typical of acontrolled solenoid launch: the drive pulse, drive current, armaturevelocity, armature position, and induced voltage.

FIG. 2 illustrates sensitivity of the traces of FIG. 1 to a 5% increasein drive pulse width.

FIG. 3 illustrates sensitivity of the traces of FIG. 1 to a 5% decreasein drive pulse width.

FIG. 4 shows families of curves like FIG. 1 for differing preload forcesaffecting launch, as well as threshold functions used to determine adesired drive pulse width for a specified armature travel.

FIG. 5 shows the drive and data acquisition hardware needed for launchcontrol as illustrated by FIG. 4.

FIG. 6 illustrates a nonlinear continuous analog servo control circuitto move a solenoid armature to a target and hold it there.

FIG. 7 illustrates an oscillating controller circuit with switch-modeoutput to perform the same function as in FIG. 6, but with greaterelectromechanical efficiency.

FIG. 8 illustrates linearizing circuit approximations that simplify thecircuit of FIG. 7 while retaining most of the functionality of the FIG.7 circuit. Integral control is based on solenoid current rather thanposition.

FIG. 9 illustrates the consolidation of the two integrators of FIG. 8into a single integrator, where servo feedback correction results inindefinite operation without integrator signal drift.

FIG. 9 a illustrates the FIG. 9 circuit modified to use position sensingfrom a permanent magnet and Hall effect device instead of a positionestimate based on current.

FIG. 10 illustrates a circuit functionally similar to that of FIG. 9except for lack of a current sense resistor and differentialamplification, use of sampled sense coil outputs to infer current, anduse of resonating circuitry to provide precise measurement of armatureposition, including when an electromagnetic force is being exerted.

FIG. 11 illustrates parameter traces, against a time axis, typical ofoperation of the circuit of FIG. 10: the switching drive waveform, coilcurrent, sampled current, sampled current derivative, velocity,position, induced voltage, and magnetic flux.

FIG. 12 illustrates a nonlinear oscillating controller circuit thatinfers armature position from sampled current slope and computesinequalities involving a ratio and a square-law function in the logdomain.

FIG. 13 a is a top view of a flat spring utilized with a pot coresolenoid.

FIG. 13 b is a perspective cutaway mechanical drawing of a pot coresolenoid with flat spring suspension.

FIG. 13 c is a cutaway mechanical drawing of a pot core solenoid withflat spring suspension, in an unenergized position.

FIG. 13 d is a cutaway mechanical drawing of a pot core solenoid withflat spring suspension, in an energized position.

FIG. 14 is an elevation section mechanical drawing of a fluid pumpingand volume measurement system using a fluid cassette interfaced to twovalve actuation solenoids and a solenoid for combined pumping, volumemeasurement, and bubble detection.

FIG. 15 illustrates a circuit similar to FIG. 9 except driving asolenoid with permanent magnets for hovering or levitation at near-zeropower consumption, and with the switching amplifier modified for bipolaroperation.

FIG. 16 illustrates a servo system for two-point magnetic levitation andpropulsion of a monorail car suspended below a track.

SOLENOID PHYSICS AS APPLIED TO THE INVENTION

The mathematical formulas to be derived will be based on a fewsimplifying assumptions that, in engineering practice, are sometimesrealized. It turns out that these assumptions are best realized for anew class of electromagnetic solenoid designs that are optimized forsoft landing, as well as for options of two-point and four-point landingcontrol (to be described later). It is difficult to measure electronicparameters adequate for servo control from a solenoid that has a lowelectromechanical efficiency. It will be seen that transformer-gradeferrites can be used in constructing fast-acting, energy-conserving,quiet solenoids whose electromagnetic characteristics are virtually“transparent” to a dynamic controller, yielding high-quality measures ofmechanical position and velocity. The mating faces of existing designsfor pot cores, E-E and E-I cores, U-U and U-I cores, are very welladapted for employing these components as electromechanical solenoidparts. The conductivity of iron in conventional solenoids permits eddycurrents, which effectively limit the bandwidth for valid determinationof position and velocity, as well as the bandwidth for quick closurethrough the inefficient region near full-open magnetic gap. Corefabrication from sintered powdered iron substantially overcomes theseconductivity problems. Poor closure of the flux path further complicateselectronic inference of position and velocity for feedback control,while simultaneously compromising electromechanical efficiency.Separating out these issues, then, there are three important assumptionswhose relative validity affects both the validity of the mathematicalderivations to follow, and the stability and precision achievable (oreven go/no-go feasibility) in a soft landing servo system or launchcontrol system:

1) For fixed shuttle position, solenoid behaves like a linear inductor.

Discussion: This is to validate the textbook inductor energy formulaE=½I²L. It is well known that ferromagnetic core materials are highlynonlinear, but when a small air gap is incorporated into an inductordesign, its performance becomes very linear until the core material ispushed well up along its saturation curve. What is happening is that theair gap has a linear B vs H relationship, and the magnetic reluctance ofthe air gap dominates the total reluctance of the magnetic circuit.Commercial solenoids approximate linear inductors for all shuttlepositions, except when pushing the maximum limits of force, since thereis always enough effective air gap in the magnetic loop to wipe out corenonlinearity except in deep saturation at maximum forces. If a solenoidis designed intentionally for a very small effective gap when theshuttle is pulled in, e.g., to minimize holding current, then theequations to be shown below may be slightly inaccurate for the last fewpercent of travel before full closure of the solenoid gap.

2) Solenoid has no memory, so magnetic energy “now”=function of electriccurrent “now”.

Discussion: Two phenomena might invalidate this assumption: magnetichysteresis, and eddy currents. Referring to assumption #1, concerningnonlinearity, the magnitudes of hysteresis effects are generally smallerthan effects of saturation for solenoids operating at comparatively highflux densities (as is inevitable if a solenoid is reasonably compact forthe mechanical energy of its stroke). Thus, air gaps wipe out hysteresiseffects in a similar way to wiping out nonlinearity effects, resultingis comparatively “memory-free” magnetic performance. If eddy currentsare of sufficient magnitude, they will partially cancel the effect ofcurrent flowing into the solenoid leads in a time-dependent manner. Themagnetic energy is a function of all currents, including eddy currents.At low frequencies, where magnetic skin depths are larger than thedimensions of conductive solenoid parts, the time constant fordissipation of eddy currents will be shorter than the time constant forchange in drive current, and there will be little eddy current buildup.At high frequencies, with shrinking magnetic skin depths, material atskin depth or deeper will be shielded from the coil fields and thuseffectively removed from the magnetic circuit, causing degradedperformance and poor correlation with the mathematical model to follow.Ferrite solenoids will be effectively immune to eddy current effects.

3) The distribution of magnetic flux linking the winding does not changewith solenoid position.

Discussion: In the derivations below, magnetic flux is treated as asimple scalar quantity with respect to inductance and back-EMF, as ifthe same flux links every turn in the winding. If the flux distributionis non-uniform, some turns get more flux than others, but the analysisis still valid for being based on an “effective” number of turns, solong as that number is constant. If the flux distribution through thewindings changes significantly when the shuttle position changes andalters the magnetic gap, then the effective number of turns couldchange, violating the modeling assumptions. Furthermore, in designs thatemploy separate windings for generating and sensing magnetic flux, theremay be a somewhat variable relationship between actuation and sensing asflux patterns in space change with changing shuttle position. There willinevitably be some gap-dependent redistribution of flux in the coil orcoils, causing minor error in the mathematical model and in the controlrelationships between drive and sense windings. These issues arebelieved to be of minor practical importance in a controller contextwhere, for most of the flight path of a solenoid shuttle, only veryapproximate control is required. As the shuttle approaches the positionof full magnetic closure, more precise control of the flight path isrequired to achieve soft landing, but in that region near magneticclosure, virtually all magnetic flux will be confined in the corematerial, totally linking drive and sense windings. Deep core saturationwill cause greater magnitudes of flux redistribution, introducing errorinto the analysis for certain operating conditions that push theenvelope of solenoid operation.

Solenoid Force Equations

The derivation of the following formulas may be explained by a gedankenexperiment: Assume that the solenoid winding is of superconducting wire,so that mathematically we ignore the effects of electrical resistance,which can be reintroduced separately, later. Imagine that, with thesolenoid shuttle position fixed, voltage is applied until the current“I” reaches a Specified level, at which time the total magnetic energyin the solenoid isE _(mgn)=½I ² L for magnetic energy “E_(mgn),” current “I,” andinductance “L.”  1]

This is the textbook formula for a linear inductor. Now, short thesuperconducting winding, allowing current to continue circulating withno external connection that would add or remove electrical energy.Theory says that a superconducting surface is an impenetrable barrier tochanges in magnetic flux, since induced currents at zero resistance willprevent the flux change. By extension, a superconducting closed loop orshorted winding is an impenetrable barrier against change in the totalflux linking the loop, for if flux starts to change incrementally, theflux change will induce a current change in the superconductor thatcancels the flux change. With no electrical energy entering or leavingthe system through the wires, the sum of magnetic field energy plusmechanical energy must remain constant. Imagine that the solenoidshuttle pulls on an ideal spring that just balances the magnetic force“F” acting on the shuttle. We assume sufficiently slow motions thatthere is negligible kinetic energy and negligible acceleration force, sothat magnetic force matches spring force in magnitude. We define “x” asthe coordinate of the solenoid shuttle, such that an increase in “x”corresponds to an increase in the magnetic gap. We will convenientlydefine “x=0” as the position of full magnetic closure, giving maximuminductance. Magnetic force “F” pulls to close the magnetic gap andreduce “x,” while the equal but opposite spring force pulls to open themagnetic gap and increase “x.” We define “F” as a negative quantity,tending to reduce “x” and close the gap. If the shuttle moves a positiveinfinitesimal distance “dx,” the spring does work to pull the solenoidmore open, so the spring loses energy. Defining “E_(mch)” as mechanicalspring energy, and given a negative magnetic force “F” balanced by anequal but opposite spring force, a positive travel “dx” result in anegative change in mechanical energy:dE _(mch) =F·dx for mechanical energy “E_(mch),” force “F,” distanceincrement “dx.”  2]

When a total magnetic flux Φ links n turns of a solenoid coil, voltageacross the coil has two expressions:V _(L) ,=L(dI/dt) inductive voltage “V _(L)” from inductance and currentchange with time “t”  3]V _(L) =n(dΦ/dt) inductive voltage from turns number “n” and change offlux “Φ” with time  4]

Setting the right hand terms of Eqs. 3 and 4 equal to each other andintegrating with respect to time yields:I·L=nΦ different expressions for “momentum” of inductor involt-seconds  5]

Assuming a superconductive shorted winding is equivalent to assumingV_(L)=0, in which case Eq. 4 implies that the flux Φ is constant overtime:Φ=Φ₀ flux is constant through time for shorted superconductivewinding  6]

With Eq. 6, Eq. 5 implies the constancy of the product I·L through time:I·L=I ₀ ·L ₀ for constant reference values I ₀ and L ₀, assuming V_(L)=0  7]

For this special shorted winding condition, substituting Eq. 7 into Eq.1:E _(mgn)=½I(I ₀ L ₀) Assuming V _(L)=0  8]

Under these conditions, the differential in magnetic energy from Eq. 8is:dE _(mgn)=½(I ₀ L ₀)dI assuming V _(L)=0  9]

With no electrical power entering or leaving the system, the sum ofmagnetic plus mechanical spring energy is a constant, which means thesum of the differentials is zero:dE _(mch) +dE _(mgn)=0  10]

Substituting in Eq. 10 from Eqs. 2 and 9:F·dx+½(I ₀ L ₀)dI=0  11]

Dividing through by the differential in distance, dx, in Eq. 11, andrearranging yields:F=½I ₀ L ₀(dI/dx)  12]

Using Eq. 7, we drop the subscripts from “I” and “L” in Eq. 12:F=½IL(dI/dx)  13]

Differentiating both sides of Eq. 7 with respect to x yields theexpression:L(dI/dx)+l(Dl/dx)=0  14]

Solving for dl/dx in Eq. 14 and substituting this expression in Eq. 13yields:F=½I ²(dL/dx)  15]Observe that “L” is a decreasing function of “x,” so that “F” and“dL/dx” are both negative. Inductance is high when the magnetic gap isclosed, so that a small current produces a large magnetic flux. Eq. 15is based on conservation of energy with an equilibrium force balance anda zero-resistance coil. The expression has general validity, however,under more complicated conditions. Taking the total derivative of Eq. Iwith respect to “x” yields:dE _(mgn) /dx= ½I ²(dL/dx)+IL(dI/dx)  16]

Solving Eq. 14 for “dI/dx” in terms of “dL/dx” and substituting into thesecond term of Eq. 16 gives a negative contribution of “−I²(dL/dx),”twice the size of the positive term, yielding:dEmgn/dx=½I ²(dL/dx)  17]

Substitution from Eq. 15 now yields:dE _(mgn) /dx=−F  18]

This serves as a consistency check. Force is negative, or attractive, ina solenoid, always tending to close the magnetic gap and drive positive“x” toward zero, so “−F” is positive. Eq. 18 therefore indicates thattotal magnetic energy in a solenoid with a shorted superconducting coilis an increasing function of gap. A spring pulling the gap open doeswork, which is transformed into magnetic energy. Inductance is reducedwith increasing gap, but current is increased to keep the product ofcurrent and inductance, “IL,” constant (recalling Eq. 7). With constant“IL,” the energy product “½I²L=½I(IL)” is dynamically linear withcurrent “I” and undergoes a net increase with increasing gap. Going inthe opposite direction, if the magnetic circuit in a solenoid becomes avirtual “short circuit” at full gap closure, meaning that there are noair gaps to be bridged by magnetic flux and the relative permeability ofthe magnetic material is very high (figures of 1000 to 100,000 arecommon), then both current “I” and the energy product “½I²L” are drivendynamically to near-zero as the gap closes. This is true not only forthe idealized case of a solenoid with a shorted superconducting windinginitialized at some current before shorting, but for a real coil withelectrical resistance and an applied drive voltage. Focusing attentionnot on voltage and current and changing inductance, but rather on thenet magnetic flux, “Φ,” that travels through the magnetic circuit, thenfor a solenoid gap approaching zero, magnetic force is more or lesslinear with the square of flux, “Φ²” There is a natural “inertia”resisting changes in “Φ,” namely, the tendency for changes in “Φ” togenerate compensatory changes in coil current and, in conductivemagnetic materials, compensatory transient eddy currents. Thus, thecombination of resistive voltage drop and coil drive voltage generates atime rate of change of flux, “dΦ/dt,” but not an instantaneous responsein “Φ.”

Solenoid manufacturers typically publish families of curves showingforce as a function of magnetic gap for various coil voltages. Thesecurves bend steeply upward as the gap goes to zero, their slopes beinglimited at high coil voltages by magnetic saturation. It is common forthe magnetic circuits in solenoids to include a significant non-closingnet air gap, usually residing partly across an annulus between statoriron and the shuttle, and partly across a cushion or minimum air gapmaintained at the end of the shuttle, e.g., by a mechanical stop locatedaway from the critical site of magnetic closure. Experience has shownthat allowing uncushioned magnetic parts to impact together generatesnoise, shock, and some combination of surface damage, work hardening,and magnetic hardening of the material near the impact site. Magnetichardening results in retention of a permanent magnetic field after thesolenoid current is removed, and sticking of the shuttle in itsfull-closed position. Eliminating air gaps and pushing the design towardfull closure of the magnetic flux loop would seem to invite problems ofuncontrollable dynamics and a worsening singularity where force tendstoward infinity as the gap closes. These appearances are deceptive,being based on steady state relationships among voltage, gap, and force.Dynamically, as a magnetic solenoid gap closes, flux and force tend notto change rapidly, and solenoid current tends to be driven toward zerowith closing gap because the solenoid naturally resists abrupt change intotal magnetic flux.

The alternative to mechanical prevention of impacting closure of amagnetic gap is dynamic electronic control, taking advantage ofinherently favorable dynamic properties of the system and employingservo feedback to avoid impact. The optimum physical design of asolenoid changes substantially in light of the possibilities for dynamicelectronic control. If there is full magnetic closure, then the point offull mechanical closure becomes virtually identical (typically withintenths or hundredths of a millimeter) with the point of zero magneticreluctance, so that the target for a zero-impact soft landing controlleris readily and consistently identified. With full closure, the holdingcurrent needed to keep a solenoid closed under mechanical load becomesalmost vanishingly small. If parts mate too well, there can be problemsof sticking due to residual magnetic flux at zero coil current, evenwith undamaged, magnetically soft materials. If needed, a little ACwiggle to the coil current will reliably unstick the shuttle—a functionthat needs to be automated in the controller implementation. Expandingon a previous statement of definition, the combined strategies ofelectromagnetic design, including flux-sensing coils as well as drivecoils, and including coordinated electromagnetic, mechanical, andelectronic design (including analog and digital software parameters) arecollectively called “soft landing.” Related to soft landing, asmentioned, are the strategies and designs for two-point landing andfour-point landing, which may optionally be combined with soft landingto achieve good electromechanical performance within a simplified anderror-tolerant mechanical design.

An Approximate Model for Inductance Versus Gap

Eqs. 19 and 20 give an approximate model for inductance “L” as afunction of gap “x.”L=μ ₀ n ² A/x _(eff)  19]

Eqs. 19a, 19b, 19c, and 19d, easily derived from Eq. 19, are includedhere for completeness. Solving first for the effective magnetic gap interms of inductance:

 xeff=μ ₀ n ² A//L  19a]

If inductance “L” is determined from measurement of a resonantfrequency,ω=2πf  19b]for measured frequency “f” in Hz giving “ω” in seconds^(−I), where theunknown “L” is resonated with a known capacitance “C”, then recallingthe basic resonance formula,ω²=1/LC  19c]it follows from Eqs. 19a and 19c that:x _(eff=μ) ₀ n ² Aω ² C  19d]

Eq. 19 is the formula for inductance with a “pillbox” magnetic field,where the magnetic circuit has no magnetic resistance except across aspace between parallel circular plates of area “A” and spaced by thedistance “x_(eff).” The turns count is “n” and the permeability of thegap volume is μ₀. The formula is based on a hypothetical magnetic fieldthat is constrained not to spread out in the space between the plates,but instead is confined to a cylindrical path (e.g., as if by asuperconducting cylinder). In a realizable situation, the performance ofan actual gap “x” between parallel surfaces of a magnetic conductorapproaches the ideal the assymptotic limit of a small gap, i.e.,“x_(eff)/x→1” as “x→0,” in which limit the field lines become parallelexcept for a shrinking “bulge” region around the area perimeter, wherethe width of the bulge shrinks in proportion to the height “x.” As thegap widens, the field spreads out over a larger effective area than theactual area of the parallel plates, thus causing theinductance-determining ratio “A/x_(eff)” to exceed the physical ratio“A/x.” This is modeled not by increasing the area “A” in the formula,but instead by reducing “x_(eff)” to a value smaller than the actual gap“x as in approximate Eq. 20:X _(eff)=(x ₀ /K)(1−1/1/(1+(x+x _(min))/x ₀)^(K)) approximately  20]

The inverse of Eq. 20 is also useful:x=x 0·((1/1−K·x _(eff) /x ₀)1/K)−1)−x_(min) approximately  20a]

Given electrical measurements to determine either inductance “L” or theradian frequency “ω” that resonates with a known capacitance “C”, thenEq. 19a (from “L”) or 19d (from “ω”) yields a value for “x_(eff)” whosesubstitution into Eq. 20a yield the geometric gap “x”. Discussion isprovided later for dynamic determination of inductance “L” fromtime-integration of a magnetically-induced voltage, and fordetermination of “ω” from ringing measured in a driver/sensor circuit.

When actual “x” goes to zero, there is some residual resistance(specifically: reluctance) to the magnetic circuit, associated withsmall air gaps, with imperfect mating of the stator and shuttle wherethey close together, and with the large but finite permeability of theferromagnetic material in the flux path. This resistance is equivalentto a small residual air gap x_(min). Eq. 20 is designed so that theparameter “x_(eff)” is asymptotic to the sum “x+x_(min)” as that termgoes to zero. As gap “x” increases, “x_(eff)” begins to increase moreslowly than “x,” at first due to the spreading of the magnetic fieldover an increased effective area. As the solenoid shuttle is furtherremoved, flux begins to bridge across gaps in the solenoid structureuntil, when the shuttle is completely removed, i.e. as “x→∞,” thereremains a finite effective distance that magnetic flux must span,jumping between magnetic surfaces with no help from the permeability ofthe shuttle. This asymptotic limit is “x₀/K.” This limit is unimportantto the practical modeling of a solenoid, since the shuttle in apractical solenoid is only operated over a limited range of travel. Whatis important is that the scaling parameters “x_(min),” “x₀,” and “K” beadjusted for the best fit to empirically measured inductance over theintended range of travel for the variable. “x.” Once this data fit isperformed for a particular shape of magnetic core and shuttle, theresults are readily extrapolated to other sizes having the same shape.The exponent “K” will be a characteristic of the shape. The lengthscaling parameter x₀, is some fraction of a specific dimension of theassembly. For example, for a typical shape of pot core, with one halfserving as the stator and the other half serving as the shuttle, a goodfit is obtained by setting K=1.5 and x₀=16D) where “D” is the diameterof the center pole piece. The value for x_(min) depends strongly on howaccurately the surfaces mate, but for a tested pot core with an outsidediameter of 50 mm, the ratio x_(min)=0.01x₀ was obtained. The practicalresult is that the minimum effective gap is quite close to zero.

A valuable approximate formula for force is derived from substitutingfrom Eqs. 19 and 20 into force Eq. 15. First expanding Eq. 15 in termsof “x_(eff)”.F=½I ²(dL/dx _(eff))(dx _(eff) /dx)  21]

Differentiating Eq. 19 gives an expression for the first derivative termof Eq. 21:F=−½I ²(L/x _(eff))(dx _(eff) /dx)  22]

Differentiating Eq. 20 gives an approximation for the last term of Eq.22:F=½I ²(L/x _(eff))(1/(1+(x+x _(min))/x ₀)^(K+1)) approximately  23]

Expanding “L” from Eq. 19 in Eq. 23:F=−½I ²(μ₀ n ² A/x _(eff)2)(1/(1+(x+x _(min))/x ₀)^(K+1))approximately  24]

In is not useful to show further expansion of Eq. 24, since nosimplifications arise to boil the expanded result down to a simplerformula. Since “x_(eff)” is asymptotic to “(x+x_(min))” for smallvalues, and since the last term in Eq. 24 approaches unity for smallvalues of (x+x_(min)), Eq. 25 is an asymptotic approximation to Eq. 24:F=−½I ²μ₀ n ² A/(x+x _(min))² approximately  25]

Not obvious without numerical computation is that Eq. 25 is asurprisingly good approximation of Eq. 24 over the entire range of thenon-dimensional distance parameter “(x+x_(min))/x₀” that is likely to beuseful in engineering computation. For K=1.5, Eq. 25 overestimates Eq.24 by just over 5% when the non-dimensional distance parameter“(x+x_(min))/x₀” reaches 1.0, and by just over 1.7% for the distanceparameter at 0.5. Noticing that in designs that close the magneticcircuit tightly, “x_(min) is a small fraction of the useful range of “x”we can write an even simpler approximate expression that aids in seeingimportant physical relationships:F=−½I ²μ₀ n ² A/x ² approximately  26]

Dissipation of power in a solenoid coil is I²R for resistance “R.” Forceis linear with power dissipation. Force is also linear with pole facearea. If a solenoid is scaled up in size while retaining the same numberof turns, “n,” and adjusting the wire gauge to fit the larger space,then the increased cross-section of the wire outpaces the increase inwinding length, so that resistance varies inversely as the lineardimension “D” of the solenoid. The effect of reduced resistancereinforces the efficiency advantage of increased area as scale isincreased. The increase of solenoid mass with size reduces theefficiency advantage in a configuration that uses a much reduced holdingcurrent after solenoid closure, because the greater mass of a largersolenoid tends to make it respond more slowly and require more time inthe inefficient wide-open range. What is especially apparent is thereciprocal square of solenoid gap in the denominator of Eq. 24. Theratio of force/power is much more favorable for small gaps, and smallgaps will be closed more quickly, meaning that reduction to a holdingcurrent occurs more quickly. These considerations are summarized in theproportionalities expressed by Eqs. 27 through 27c, based on Eq. 26(complete derivation not provided here). Eq. 27 describes, for aspecified output of mechanical Energy per stroke, “E_(s),” how the Powerdissipated in electrical resistance, “P_(d),” varies as a function ofthe stroke length “x” and of a characteristic linear dimension “D0”(e.g., the diameter of a pole piece):

 P _(d) ∝x·E _(s) /D ³ proportionality based on approximate Eq. 26  27]

Energy per stroke “E_(s),” is defined for tills derivation as the force“F” developed at gap to x” multiplied by that gap, i.e. “F·x,” thoughthe same proportionality holds true if “F” varies as a function of thestroke going from “x” to zero in such a way that the shape of the forcecurve is maintained with resealing of “F” and “x” such that the ratio ofactual stroke energy “E_(s)” to the product “F·x” is maintainedconstant.

Moving from rate of power dissipation to net energy to accomplish astroke, if the acceleration of the shuttle is limited by the mass “M” ofthat shuttle, and if proportional scaling of the moving part ismaintained so that “M” varies in proportion to the cube of thecharacteristic dimension “D,” i.e. M∝D³, then one obtains a stroke time“t_(s)” whose proportionality to the parameters of the system isexpressed by:t _(s) ∝x√{square root over (D ³ /E _(s) )}  27a]

Under the circumstances where solenoid inertia is the limiting factorfor stroke time, such that Eq. 27a is valid, then the Energy dissipatedin electrical resistance, “E_(d),” varies in proportion to the product“P_(d)·t_(s),” as shown in the following equation:E ^(d) ∝x ² √{square root over (E _(s) /D ³ )} absolute loss,acceleration limited by solenoid mass  27b]

Eq. 27c expresses the same proportionality as a loss ratio:E _(d) /E _(s) ∝x ² /√{square root over (E _(s) ·D ³ )} loss ratio,acceleration limited by solenoid mass  27c]

Since mass “M” varies as “D³” we can rewrite Eqs. 27b and 27c in termsof “M”:

 E _(d) ∝x ² √{square root over (E _(s) /M)} absolute loss, accelerationlimited by “ M”  28]E _(d) /E _(s) ∝x ² /√{square root over (E _(s) ·M)} loss ratio,acceleration limited by “ M”  28a]

If a solenoid drives a load through a lever that provides some ratio ofmechanical advantage or disadvantage, so that solenoid stroke length “X”may be varied at will in a design while maintaining a constant curve offorce versus stroke position at the load side of the lever, and if thesolenoid mass is the limiting factor for acceleration, then the aboveformulas for “E_(d)” apply. If the mass on the load side of the lever ispredominant in limiting acceleration, then Eq. 27a is invalid, stroketime “t” becomes more or less a constant, and stroke energy becomesproportional to that constant stroke time “t” multiplied by “P_(d)” ofEq. 27. Many real world designs will lie somewhere between theproportionalities for “P_(d)” and for “E_(d).” The situation wheresolenoid inertia is rate-limiting places a higher efficiency, premium onreduced stroke length, whereas the situation where the load israte-limiting places a lesser premium on reduced stroke length and ahigher premium on increased solenoid size, expressed either by acharacteristic dimension “D” or a characteristic mass “M.” In eithercase, these formulas make it clear that to obtain work from a solenoidat high efficiency, and provided that it is feasible to trade offreduced stroke for increased force at constant stroke energy, then thereis a strong advantage to keeping the stroke length as short as possible.For a fixed size of solenoid, this implies driving the solenoid toachieve the largest possible force. Force varies as “B²,” the square ofthe field strength at the pole faces, and saturation of the corematerial of the solenoid places a constraint on the maximum magnitude offield strength “B.” Optimization by reduction of stroke “x” and increaseof force “F” to maintain a constant energy product “F·x” at constantdimension “D” will obviously drive the magnitude of “B” upward untilsaturation becomes a limiting factor in the design. One thus encountersa boundary to the application of the above equations for optimization.Working at the saturation boundary, there is an advantage to increasingsolenoid size and poleface area, which at constant stroke energy allowsone to reduce stroke “x” inversely as the square of dimension “D,” thuskeeping the swept stroke volume “x·D²” constant. In this case, x²∝1/D⁴,and 1/D⁴ is multiplied by 1/D^(1.5) from the denominator of Eq. 27b or27c to yield a net scaling of dissipated energy as the power law1/D^(5.5) for the solenoid-inertia-limited case. Similar considerationslead from Eq. 27 to a dissipated energy power law 1/D^(5.0) where stroketime is load-limited. Under all the circumstances described above, thereis a strong efficiency advantage in using a big solenoid with a shortstroke for a task requiring a given stroke energy, where this isfeasible. When one reaches a minimum practical stroke, e.g., because ofdimensional tolerances, then further increases in solenoid size at afixed stroke “x” yield much more marginal efficiency returns.Diminishing returns of a different sort are encountered in a solenoid isso efficient as a motor that dissipated energy “E_(d)” is no longerlarge compared to stroke energy “E_(s),” an operating region whereefficiency is so high that there is little net energy to be saved byfurther efficiency improvement. This happy situation is seldom realizedin practice.

It is well known that metallic iron and magnetic steel alloys have asubstantially higher saturation B-field than ferrites, e.g., about 2.0Teslas for iron as against about 0.5 Teslas for ferrites, roughly a4-to-1 advantage. This translates into roughly a 16-to-1 advantage formaximum force at a given size, e.g., a maximum characteristic dimension“D.” Maximization of force, however, is quite different frommaximization of efficiency. Eqs. 27 through 28a imply an efficiencyadvantage to making a solenoid larger than the minimum size dictated bycore saturation. Where efficiency optimization drives the Solenoid sizelarge enough that saturation will not occur in a ferrite core, thenferrite has the advantage of lower density than iron, implying a quickerstroke. While magnetic core hysteresis loss is a major consideration intransformer design, hysteresis is a very minor issue in solenoiddesigns, since the magnetic reluctance of the air gap is predominant incontrolling the relationship between winding ampere-turns and the fieldstrength that determines force. Thus, sintered powdered iron cores,which are cheaper but more lossy than ferrites in high frequencytransformers, perform about as well as ferrites in solenoids at low fluxdensities while providing a substantially higher saturation field. Inthe servo control and measurement strategies to be described below,based on measurements of the voltages electromagnetically induced insolenoid windings, the electrical conductivity of solid iron or steelsolenoid parts can present substantial problems for accuratedetermination of solenoid position. These problems are overcome to somedegree with higher-resistivity powder metal cores and even more withferrite cores. Where extremely high acceleration is demanded in asolenoid core, e.g. in moving an automotive engine valve through aprescribed stroke in a time period constrained by high engine RPMs, theniron or powder metal solenoid parts will accelerate faster than ferriteparts due to the higher achievable flux density.

The above proportionality optimization equations are based on constantshape of the solenoid pole pieces. When varying taper of the pole facesenters the optimization process, this adds considerable complication tothe analysis. For a given size of solenoid and a given stroke energyrequirement, use of tapered pole pieces confers little advantage ordisadvantage (the particulars depending strongly on the pattern ofsaturation of inductor material) except where constraints demand a longstroke, in which case tapered pole pieces can offer some advantage.There is some advantage to shaping a solenoid so that most of themagnetic flux path is in the stator, to minimize shuttle mass andthereby minimize the duration of a stroke. Solenoids whose shuttles arecylinders many diameters in length are at a disadvantage for massminimization. This patent specification will disclose some flattersolenoid geometries that help maximize gap area, minimize moving mass,and in some contexts simplify the task of guiding the motion of thesolenoid shuttle, avoiding the traditional bushing design that cansuffer from wear problems in high-duty applications.

Electromechanical Behavior of a Solenoid

In deriving Eqs. 1 through 26, we conceptually prevented dissipativeelectrical energy transfer by assuming a resistance-free, shorted coil,thus simplifying the physics. The derivation of Eqs. 27 through 28a, notshown completely above, introduced electrical resistance. The followingderivations conceptually permit exchange of electrical energy with themagnetic circuit via coil current and the combination of externallyapplied voltage and internal voltage drop due to resistance. Theinductive voltage of Eq. 4, which promotes change in coil current, isprovided by an external drive voltage from which is subtracted aresistive voltage loss:

 V ₁ =V _(ext)−1·R  29]

The resistive voltage drop “I·R” neglects skin effect, which is usuallynegligible in coil windings at frequencies for which it is possible toovercome the mechanical inertia of a solenoid shuttle and inducesignificant motion. Skin effect may be significant in metallic alloys ofiron and nickel (the primary ferromagnetic components of solenoids),cobalt (the more expensive ferromagnetic element, less likely to finduse in solenoids), chromium (an anti-rust alloying component), and theother trace elements commonly appearing in solenoid alloys. Ferrites donot share this problem. High magnetic permeability in a conductivematerial has the effect of reducing skin depth very substantially, sothat skin currents in the shuttle and stator components of a solenoidcan transiently shield underlying magnetic material from a coil fieldand reduce the dynamic response of the solenoid. Reiterating cautionnumber 2 under “SOLENOID PHYSICS AS APPLIED TO THE INVENTION,” theperformance analysis that follows will, for some geometries andmaterials, be overly optimistic concerning the speed of solenoidresponse and concerning applicability of the methods being derived herefor servo control. This author and a colleague have measured solenoidsin which change of inductance with shuttle position is dramatic andreadily observed over a broad band of frequencies, and other solenoidsin which impedance is almost purely resistive in and below the audiofrequency band, with shuttle-position-indicating changes in theinductive component of impedance being detectable only with effort atsorting out in-phase and quadrature-phase impedance components.Solenoids in the latter category are not good candidates for the kind ofcontrol described herein.

Eq.7, indicating the constancy of the product “I·L,” implies a formulafor the partial derivative of current with respect to inductance when xvaries. To get the total derivative of current with respect to time, weneed to consider the partial derivative with time associated withinductance L and voltage V_(L), plus the partial derivative of currentwith inductance multiplied by the change of inductance with time:dI/dt=∂I/∂t=∂I/∂L·dL/dt  30]

The partial derivative of current time is the effect of applied voltage,the familiar expressed for fixed inductances:∂I/∂t=V _(L) /L  31]

The partial derivative of current with inductance is derived from Eq. 7:∂I/∂L=−I/L  32]

Substituting Eqs. 31 and 32 into Eq. 30 yields:dI/dt=V _(L) /L−(I/L)(dL/dt)  33]

Expanding V_(L) according to Eq. 29:dI/dt=(V _(ext) −I·R)/L−(I/L)(dL/dt)  34]

A finite difference expression equivalent to Eq. 34 as time increment“dt” approaches zero suggests an approach for numerical integration:I _(n+1) =I _(n)(Ln/L _(n+1))+dt·(V _(ext) −I·R)/L  35]

Our mathematical description is almost sufficient to simulate theresponse of a solenoid, so that the understanding gained can be used todesign the analog circuit operations and digital methods of a workingcontroller. Eq. 15, defining force as a function of current andinductance, will be needed, as will Eqs. 19 and 20, defining inductanceas a function of gap “x,” plus either Eq. 34 or 35 to simulate thechanging electric current, and finally an equation for shuttleacceleration, including a description of the mechanical load. One loaddescription is incorporated into Eq. 36, which describes theacceleration of a shuttle of mass “M” driven by magnetic force “F′” andby a spring having linear spring rate “K1” and biased from an unstressedshuttle position “x₁” to the actual present shuttle position, “x:”d ² x/dt ²=(F+K1(x ₁ −x))/M  36]

Having developed the tools to model the motion of a solenoid, we requiresomething in addition to exert servo control for soft landing: a methodfor measuring or inferring shuttle position. An obvious approach takenin past art is to provide an extra transducer to serve solely as aposition sensor. It is feasible, however, to infer shuttle position, ora useful smoothly-varying monotonic function of shuttle position, frominductance measurement or inference from related parameters. Theparameter “x_(eff)” appearing in Eq. 19, and approximated by Eq. 20 as afunction of “x,” may be inferred with reasonable accuracy frommeasurement of the electrical response in solenoid windings. Forachieving soft landing, it is not necessary to transform “x_(eff)” intothe linear Cartesian coordinate “x.” The only advantage of such atransformation is to obtain a position variable for which the effectivevalue of mass “M,” e.g., in Eq. 28, is a constant. In the nonlinearcoordinate “x_(eff),” the effective mass will vary somewhat, alteringthe equations of motion but not preventing a control method fromfunctioning to bring a solenoid shuttle to a target position and land itwith a low velocity at contact.

A pair of readily determined parameters to define “x_(eff)” consist oftotal magnetic flux “Φ” and coil current “I.” Recalling Eqs. 3, 4, and5, inductive voltage V_(L) is related to both inductance and flux. Theseequations are based on a fixed inductance, but Eq. 4 is valid even fortime-varying inductance, being based on the fundamental relationshipbetween voltage and magnetic flux cutting across a conductor. Eq. 5 alsohas general validity, allowing one to solve for inductance “L” whencurrent “I” and flux “Φ” are known, including when “L” varies with time.To determine Φ during the operation of a solenoid, one has a referencepoint when the solenoid gap is fully opened and no current is flowing:Φ=0. Residual magnetism in the solenoid core material will have anegligible effect for a material with low coercive force and in thepresence of a large air gap. External magnetic fields will beinsignificant compared to the magnitudes of normal operation. The moststraightforward way to determine “Φ” dynamically through time is withall auxiliary sense winding in parallel with the solenoid drive winding.In this way, resistive voltage drop in the drive coil will be of noconsequence, and the voltage obtained from the sense winding will be agood measure of the time derivative of flux. Thus parameter can beintegrated, starting from an initialization value of zero, either byanalog integration or periodic sampling of the sense voltage andcumulative summation of the sampled values. Either the analog integralor the cumulative sum can be scaled to give a useful measure of “Φ.” Theother needed control parameter is “I,” the current that together withinductance “L” sets “Φ.” A current sense resistor is an obviousapproach. Now solving Eq. 5 for reciprocal inductance:1/L=I/nΦ  37]

The reciprocal of “L” is linear with “xeff.” Incorporating the scalingcoefficients of Eq. 19 yields:x _(eff)=μ₀ nAI/Φ  38]

As already stated, “x_(eff)” is a sufficient parameter to base softlanding control, its nonlinearities with respect to the Cartesiancoordinate “x” being of little practical consequence. For a magneticloop that closes to a very low reluctance, the offset between themechanical limit of full closure and the zero of “x_(eff)” will be oflittle consequence. Targeting landing at x_(eff)=0 and approaching zeroexponentially will result in landing in a finite time at a very lowvelocity. If the offset of the mechanical stop is significant, an offsetcorrection can be incorporated into the landing software. Mechanicalclosure is relatively easy to detect: “x_(eff)” will not become smallerwith increase in drive current.

An alternative way to determine “x_(eff)” is to make an AC measurementof inductance “L.” With electronic control of coil voltage and currentmeasurement capability, measuring inductance is a matter of determiningthe dynamic ratio of voltage variation to rate of change of current.Once the general approach has been identified, an obvious implementationis with a switching regulator to control average current. Specificcircuit examples will be given later, while the objective in theseparagraphs is to define the conceptual approach. The switching regulatorapplies DC supply voltage across the solenoid terminals in pulses.Between pulses, a transistor or diode allows current to circulate or“freewheel” through the winding, sustained by inductance and decayingdue to resistance. If current needs to be reduced faster than the ratedetermined by resistance and magnetic effects, a transistor used in the“freewheel” current path can be pulsed off while the power supplytransistor is simultaneously off. The inductively-sustained freewheelcurrent will immediately build up a voltage exceeding the DC powersupply voltage, and current will flow back into the supply through adiode, thus giving “regenerative braking.” As was shown in Eq. 32, therate of change of current with time will include a component due toshuttle motion and rate of change of inductance. In solenoids thatprovide a fairly clean inductance signal at practical regulatorswitching frequencies, the current waveform will approximate a sawtoothwave responding to voltage switching. The difference in slope betweenthe voltage-on and voltage-off conditions can then be divided into theassociated voltage swing to yield reciprocal inductance, as summarizedin Eq. 39:I/L=(dI/dt)/V defined by sampling current sawtooth driven by voltagepulses.  39]

As a solenoid approaches gap closure, current is driven to a smallvalue, so that the resistive component of coil voltage becomes a smallfraction of the externally applied voltage. If supply voltage is “Vb”and the positive current slope is designated “İ>0” then Eq. 39 isapproximated by:1/L≅(İ>0)/Vb defining reciprocal inductance during voltage pulse atsmall gap.  39a]

The relationship expressed by Eq. 39a is exploited in the embodiment ofthe invention illustrated in FIG. 11. Observe the signal waveformssketched near points in the circuit, including a sawtooth-like currentwaveform at 1100, a band-limited inverted current slope waveform labeled“−İ” at 1101, and a sampled peak waveform labeled “İ>0” labeled at 1102and corresponding to the like term in parentheses in Eq. 39a. Supplyvoltage Vb is considered constant. Thus, the sampled current-slopewaveform is used as a position variable in the servo control loop. Sinceaccuracy in this soft-landing circuit is required only on approach tozero gap, the approximation of Eq. 39a is accurate where accuracy isneeded.

As the current waveform in the figure suggests, current immediatelyafter the voltage transient may exhibit overshoot before settling into amore linear slope. Overshoot can be caused by eddy currents intransformer steel transiently lowering the effective inductance. Thecurrent slopes to subtract for Eq. 39 should be computed from data takenafter transient settling, if possible.

Eq. 19 is readily solved for “x_(eff),” using the solution forreciprocal inductance from Eq. 39:x _(eff)=(1/L)(μ₀ n ² A)  40]

Eq. 40 is just a rearrangement of Eq. 19a. The value of magnetic flux“Φ” will need to be determined from data to enable computationsdescribed below, whether this value is measured by integrating a sensecoil output, or by inference from measured current “I” and reciprocalinductance “1/L” either from Eq. 39 based on AC measurements over pulsewidths or from Eq. 19c based on ringing frequency measurements involvinga known capacitance in the solenoid circuit. In the AC measurement case,“Φ” comes from “I” and “L” most simply from dividing the sides of Eq. 5by “n”:Φ=I·L/n  41]

A potential advantage to AC determination of inductance and shuttleposition is that the result is valid even if the reference value offlux, Φ, has been lost. This situation could come up where soft landingis used not for magnetic closure, but for slowing the shuttle before itimpacts a mechanical stop at full-open, e.g., in a device that mustoperate very quietly. If a solenoid has been kept closed for a longperiod, flux in relation to current could drift, e.g., with heating ofthe solenoid. Heat can affect both magnetic permeability and theintimacy of mating of magnetic pole faces, whose alignment ormisalignment can be affected by mechanical thermal expansion. The ratioof flux to current is sensitive to both permeability change and verysmall changes in the nearly-closed magnetic gap. Another more subtleeffect is the time dependence of magnetic permeability. It is known thatfield strength in permanent magnets at constant temperature declines asa function of the logarithm of time over periods from seconds to years.“Soft” ferromagnetic materials have a similar settling behavior understeady magnetomotive force. For soft landing at full open, the“location” of the target in terms of “x_(eff)” should be known fairlyaccurately, so that velocity can be small when the target is reached,and so that the solenoid does not waste energy “hovering” in a region ofhigh power dissipation and moving slowly to find the target. An ACdetermination of position does not depend on past history, and for themagnetic circuit approaching-full-open, inductance, is a stable measureof shuttle position, with minimal sensitivity to temperature-sensitiveparameters such as core permeability.

A potential disadvantage to AC determination of inductance and positionis that in solid metal solenoids (as opposed to ferrite core solenoidsor powder metal core solenoids), high frequency inductive behavior islikely to be affected strongly by eddy currents or, to say the samething, skin effect, which will have the effect of shielding the solenoidwinding from the magnetic core, reducing inductance in afrequency-dependent manner that can make position determinationimpractical. Tracking of net magnetic flux will be much less sensitiveto skin effect than AC inductance determination, since flux is acumulative, or integral, parameter with respect to both drive voltageand shuttle velocity. Correlated with flux is current, which again is acumulative or integral parameter in an inductive system. Flux andcurrent determinations will be comparatively less perturbed byhigh-frequency skin effect. An added potential advantage of thecumulative parameter approach is reduced computation, in both digitaland analog implementations. Where a solenoid exhibits a high-Qinductance to well above the frequency of a switching controller, acapacitor may be introduced into the circuit to induce high frequencyringing, in which case the ringing frequency may be determined bywaveform sampling or by period measurement using appropriate high-passfiltering and a comparator. A sense winding coaxial with the solenoiddrive winding provides an easy way to measure either high frequencyringing or a “dΦ/dt” signal for integration to obtain “Φ.”

The derivations so far have concentrated on position measurement. Theother significant control issue is to simplify dynamic control of forceunder dramatically changing conditions of current/force response andvoltage/current-slope response. In Eqs. 37 and 38, we found that “L” and“x_(eff)” could both be expressed in terms of “I” and “Φ.” A similarreduction of force is now obtained by substituting for “L” and “x_(eff)”from Eqs. 37 and 38 into Eq, 22:F=−½(Φ²/μ₀ A)(dx _(eff) /dx)  42]

Eq. 42 is exact to the extent that the assumptions outlined earlier arefulfilled, concerning linearity, memory-free response, and consistentflux linkage of the windings. Eq. 38 provides a way to determine, fromdata, the value of “x_(eff)” at which the derivative “dx_(eff)/dx” is tobe evaluated. What is not made explicit is the relationship between gap“x” and the parameter “x_(eff).” The curve relating “x” to “x_(eff)”depends nontrivially on the detailed geometry of the magnetic circuitand can be derived empirically from inductance measurements as afunction of gap “x” for any particular solenoid, using Eq. 40 totranslate inductances into values of “x_(eff).” A useful approximationfor Eq. 42 employs the approximate model of Eq. 20, which requiresparameter values for “x₀” and “K” to flesh out the model:F=−½(Φ²/μ₀ A)(1+(x+x _(min))/x ₀)^(K+1)) approximately.  43]

The expression in “x,” “x_(min),” and “x₀” on the right of Eq. 43 can bere-expressed in terms of “x_(eff)” using Eq. 20:1/(1+(x+x _(min))/x ₀)^(K)=1−x _(eff)(K/x ₀)  44]

Eq. 38 defines “x_(eff)” in terms of measurable parameters in anexpression to substitute on the right of Eq. 44:1/(1+(x+x _(min))/x ₀)^(K)=1−(μ₀ nAI/Φ)K/x ₀)  45]

Now rearranging the right hand side of Eq. 45 slightly and substitutingthat result into the expression on the far right of Eq. 43 yields:F=−½(Φ²/μ₀ A)(1−K(μ₀ nAI/Φ)/x ₀) approximately.  46]

While Eq. 46 shows that all the data for computing F comes from flux “Φ”and current “I,” it is useful to substitute back in the expression fromthe right of Eq. 44, rearranged to express a dimensionless ratio of x's:F=−½(Φ²/μ₀ A)(1−K(x _(eff) /x ₀)) approximately.  47]

The value for “x_(eff)” comes from data via Eq. 38 or Eq. 40 (dependingon the measurement modality), but the expression of Eq. 47 clarifies thedimensional relationships. The expression on the far right of Eq. 47 isa dimensionless magnitude correction for the flux-squared term on thenear right. This magnitude correction is barely less than 1.0 for smallmagnetic gaps and generally exceeds 0.5 for the largest magnetic gapsthat are practical in solenoids. As “x” goes to infinity, i.e. when thesolenoid shuttle is completely removed, then the correction factor onthe right of Eq. 47 goes to zero as “x_(eff)” approaches its limitingasymptote. For practical control purposes, where the maximum value of“x_(eff)” is confined by the full-open limit stop on the solenoidshuttle, the correction factor can be ignored, i.e. set to unity,revealing a very simple approximation of force:F=−½(Φ²/μ₀ A) asymptotically as x→0.  48]

“Exact” Servo Control Methods

When magnetic flux is known, force is known approximately, and quiteaccurately in the gap-closure landing zone. Added information aboutcurrent yields a correction that makes the force expression accurateeverywhere. Concerning well-behaved control relationships, recall Eq. 4,which is repeated here for emphasis:V ₁ =n(dΦ/dt) (repeated)  4]

The inductive component of coil voltage, V_(L), depends only on rate ofchange of magnetic flux, independent of solenoid position. Inversely,magnetic flux varies as the linear time integral of inductive voltage,independent of shuttle motion. Approximately speaking, and fairlyaccurately for small motions in a soft landing zone, the square root ofmagnetic force varies as the linear time integral of inductive voltage,independent of shuttle motion. Eq. 38 is solved for current “I” toemphasize another relationship:I=Φ(x _(eff)/μ₀ nA)  49]

If flux were viewed as a type of current, then a solenoid would behavelike a linear constant-coefficient “inductor” with respect to “fluxcurrent.” Actual electric current is much more complicated, varying as afunction of applied voltage and solenoid shuttle position. As Eq. 49suggests, it is also possible to consider electric current as adependent variable, determined by a combination of effective shuttleposition and total magnetic flux. For setting force in a solenoid,fortunately, it is the “well behaved” magnetic flux parameter whosecontrol is important, so a good approach to servo control is to measureand control flux using relatively simple, constant-coefficient controlmeans, and consider current as a “byproduct” of control, significantonly as something that an amplifier must supply as needed to achieve thedesired magnetic flux. The demand for current, and for the extra voltageneeded to push that current through ohmic coil resistance in order tomaintain a prescribed inductive voltage V_(1.), will vary widely withchanging shuttle position. Solving for the voltage required from acontroller output at a given moment, we begin by solving Eq. 29 forV_(ext):V _(ext) =V _(1.) +I·R  50]

In a control context, current “I” will have just been measured. Thoughthe “meaning” of “I” in terms of other variables is given by Eq. 49,there is no advantage in substituting the expansion on the right of Eq.49 into Eq. 50. The controller will be targeting some rate of fluxchange, “dΦ/dt,” which will set the required inductive voltage V_(1.)according to Eq. 4. Substituting this voltage in Eq. 50 yields theproper setting for amplifier output voltage:V _(est) =n(dΦ/dt)+I·R  51]

By making the proper choice of measurements and control parameters, softlanding control is reduced to a linear third-order control problem:second order from the double integration from acceleration to positionof the shuttle, and moving from second to third order when one adds theintegration from voltage to magnetic flux. (If magnetically induced eddycurrents are substantial in the time frame of one shuttle flight, thisraises the order of the dynamic system from 3 to at least 4, which makesthe servo control problem substantially more difficult, and potentiallyimpossible if solenoid coil measurements are the sole source of flux andtrajectory information.)

Before proceeding with the control discussion, note that Eq. 51 suggestsan alternative method for measuring coil current “I” as needed in Eq. 38to solve for “x_(eff)” and, via Eq. 20a, for position “x.” If voltagereadings are taken from a sense coil with “n1” turns, the measured sensevoltage is “n1(dΦ/dt),” which multiplied by the turns ratio “n/n1”yields the inductive voltage term on the right of Eq. 51. In a switchingregulator, “V_(ext)” is set either to the appropriate power supplyvoltage for the on-condition, or to zero for the current-recirculatingcondition. The supply voltage may be a known regulated output or ameasured unregulated value. The resistive voltage term “I·R” is adjustedto include the effects of all current-dependent voltages developed inthe current path, e.g., the on-resistance of a field effect transistor,the saturation voltage of a bipolar switching transistor or darlingtonpair, or the nonlinear forward voltage drop across acurrent-recirculating diode. One might view the adjusted “I·R” voltageas “R(I)” where “R” is viewed as a nonlinear function of current “I.”With a knowledge of the two terms “n(dΦ/dt)” (as inferred from the sensecoil output) and “V_(ext)” (which is zero or a supply voltage), and witha knowledge of the resistance function “R(I)” one is in a position tosolve Eq. 51 for current “I” This solution is conceptually the simplest(and often most favorable computationally) in the recirculating modewhere V_(ext)=0, for then one does not need to know the supply voltageand one need only solve “R(I)=−n(dΦ/dt)” for current I. Operationally,one may determine current “I” and solve for position by this simplestrecirculating-mode equation during the power-off periods of any drivepulse train. One then requires only a single sense coil A-to-D channel,computing current, position, and force from a time integral (i.e. a sum)of the channel output and from the most recent instantaneous readingwhere the coil drive voltage is switched off.

Returning to the dynamic control problem, to avoid the problems ofthird-order control, the controller loop can be split into an inner,fast-acting first-order loop that exerts tight servo control over forcevia control of magnetic flux, and a slower outer second-order loop thatuses force to control shuttle position and velocity. For this outerloop, the principles of “PID” control are applicable, usingProportional, Integral, and Derivative terms. Inclusion of a significantintegral term In a PID loop controlling a second (or higher) ordermechanical system tends to introduce overshoot and ringing, which workto the detriment of energy efficiency and an ability to soft landwithout bumping at full closure (due to overshoot.) In a solenoid thatfires repetitively and can be monitored by a control microprocessor, acircuit bias can be introduced that amounts to an integral correctioncarried out over many response repetitions, rather than within the timeframe of a single actuation. The bias so determined will be closelyrelated to the expected magnitude of flux to generate an equilibriumwith load force at the landing point, either full-open or full-close. Ifthe shuttle overshoots and lands with a bump, then the required landingflux bias was overestimated for a closing gap, or underestimated for anopening gap, and will be reduced or increased (respectively) for thenext try. If the shuttle undershoots and has to be pulled in aftercoming to a stop short of the mark, then the opposite correction isneeded. One supposes, in this context, that a microprocessor controlleris monitoring solenoid performance (e.g., via analog-to-digitalconversion) and adjusting control parameters (e.g., a digital-to-analogoutput) to optimize performance adaptively. When the solenoid loadvaries significantly and unpredictably with each individual flight, amore sophisticated control method may be needed to make on-the-flyparameter corrections that anticipate landing conditions.

To expand upon the controller design, the outer loop of the controllerwill demand measurements of “I” and “Φ” from which are computed aposition “x_(eff).” This value is compared to the next-most-recentposition for estimating a velocity. In the “PID” method, an error signalis defined by a weighted sum of position error, which is theProportional term “x_(eff)-x_(tgt)” for target position “x_(tgt)” (wherethe target will be zero on somewhere near zero for soft landing onclosure), and velocity, the Derivative term, which is given by the mostrecent change in position. To the resulting error will be added anIntegral term, or bias, which is often based on experience with previoussoft or not-so-soft landings, rather than being a dynamic integral forthe present launch. The resulting “PID” sum sets a target for flux, “Φ,”which is a goal value for the inner loop of the controller. It sohappens that the square of this target flux is the actual force thatproduces accelerations. The controller does not deal directly withforce, but only indirectly in terms of the flux that is required toovercome external load forces and produce accelerations. To achieve astable system, the inner loop should converge much more quickly than thelead time constant set by the ratio of the Proportional to theDerivative term in the outer loop. To get to the target “Φ” from thecurrently measured value of “Φ” with a first order controller, arate-of-change of flux will be set as a coefficient multiplied by thedifference between the currently measured and the target flux. Thisrate-of-change appears in the first term on the right of Eq. 51.Electric current “I” will have just been measured and provides thevariable multiplier for the second term on the right of Eq. 51. Theoutput set by the controller is the left hand term of Eq. 51, “V_(ext),”and this output alone controls the process of converging to a softlanding. In a switching regulator setting, the value for “V_(ext)” maybe translated into the width of a single pulse, such that the averagevoltage over the coming controller interval including that voltage pulsewill be “V_(ext).” The time constant for the inner controller loop mightthen be set to exactly one controller interval, so that the width of asingle pulse pushes flux from the most recent value all the way to thenew target value. When the computed pulse exceeds the controllerinterval, then the pulse is set to occupy the entire controllerinterval, or most of it, and the controller will be in a slewing mode,seeking a maximum rate of change of flux.

A switching regulator driving a solenoid will typically provide onlyunipolar pulses, whose widths will become small when the solenoid isclosed. If this regulator encounters large and unpredictable loadvariations, it may find itself requiring negative pulses, to “put on thebrakes” and avoid closure impact. A switching method for “regenerativebraking” of inductively sustained coil currents, mentioned above, willbe shown in greater detail in the next section.

Spelling out the above “PID” controller approach in terms of equationsin a specific application context, imagine that there is a fixedcontroller time interval, t, at the beginning of which a pulse is fired,preset for an interval t_(p), based on the PID method. If the switchingregulator high-state output voltage is V_(h), and the low-state outputvoltage is approximately zero, allowing solenoid current to flow fromground potential to ground potential, then the applied external voltageV_(ext) can be written as an average voltage over the pulse interval:V _(ext) =V _(h)(t _(p) /t) duty cycle average voltage  52]

Rewriting the right side of Eq. 51 in terms of pulse width modulation,the controller will be seeking a change in flux, Φ, to get flux up to atarget value during one pulse interval t. This net flux change per timeinterval is substituted for the time derivative of flux on the rightside of Eq. 51, while the right side of Eq. 52 is substituted for theleft side of Eq. 51:V _(h)(t _(p) /t)=n(Φ/t)+I·R  53]

The prescription for Φ will be spelled out below. The controller willrequire solution of Eq. 53 for the pulse time interval, t_(p), to befired in order to provide the desired Φ:

 t _(p)=(n·Φ+I·R·t)/V _(h)  54]

Note that the two terms in the parentheses on the right of Eq. 54 haveSI units of volt-seconds, and are divided by an on-voltage to give apulse period in seconds. In the case of a pair of field effecttransistors (FETs) switching one end of a solenoid coil between a supplyvoltage and ground, presuming similar on-resistance for the two FETs,then it is appropriate to include the FET on-resistance as part of thenet resistance “R,” in addition to winding resistance, and then setV_(h) to the full supply rail voltage, without correction for dropacross the switching FET.

The value for Φ comes from the most recent determination of flux bymeasurement, Φ_(n) for time index “n” just passed, and a target flux,Φ_(n+1), determined as fulfilling the force requirement of the “PID”control loop:Φ=Φ_(n+1)−Φ_(n)  55]

As indicated in Eq. 48, for a magnetic gap approaching zero, forcevaries roughly as the square of magnetic flux. For a control system inwhich the landing or holding force to be expected on a given landing isestimated from the force required on recent landings, the controllerwill establish an end-point value for force or, in practice, the targetflux that was required to provide that holding force, Φ_(tgt). Thistarget flux is the integral term of a “PID” loop, but in this contextthe integral is a sum from previous landing errors, possibly based onthe most recent landing, or possibly based on an extrapolation from twoor more previous landings. Because of the square-law nature of the forceresponse, a given flux correction, Φ, will result in a larger change inforce, and therefore in acceleration, for a larger bias in the magnitudeΦ_(tgt). A linear control method based on position “x_(eff)” andvelocity “dx_(eff)/dt” would achieve different loop gains at differentlanding forces and, consequently, different end-point flux levels. Tomake the loop gains independent of end-point force (where this it mightbe relevant), we scale the system loop gain to vary inversely as theanticipated “Φ_(tgt).”

 Φ_(n+1)=Φ_(tgt)+(G/Φ _(tgt))(x _(eff) −x _(min) +τ·dx _(eff) /dt  56]

In Eq. 56, “G” is the loop gain coefficient, and “τ” is the phase-leadtime constant for the derivative controller term. The overall controllermethod includes repetitive solutions to Eq. 56, with substitution of theresult from Eq. 56 into Eq. 55, and from Eq. 55 into Eq. 54, where thepulse interval is set in order to produce the appropriate flux andforce. Values for “x_(eff)” come from earlier equations, depending onthe measurement approach (i.e. using derivative determination of “1/L”or integral determination of “Φ,” as discussed), and the time derivativeof “x_(eff)” typically comes from a finite difference over the mostrecent time interval. One can also infer a more up-to-date velocityparameter by examining the relationship of velocity to rates-of-changeof the flux and current parameters going into Eq. 38 and designing forslope measurements and computations based on those parameters and rates.As velocity approaches zero, the error term with the gain multiplier “G”goes to zero as “x_(eff)” approaches the target “x_(min).” By expressinggain as the ratio of “G” to anticipated flux magnitude, one achieves arelatively constant gain in the realm of force and acceleration. If thefactor “G” is pushed too high, the controller will become unstable dueto time lag between measurement and force response, i.e. some multipliertimes the controller time interval t, and also due to possiblehigh-order time response lags (such as skin effect) in theelectromechanical system. By varying dynamic gain adaptively as shown inEq. 56, the designer helps insure stability over a range of operatingconditions and can push the limits of loop gain over the entireoperating envelope. Where landing force does not vary significantly, thecoefficient “(G/Φ_(tgt))” can be replaced by a constant coefficientwithout compromise to the controller design. The gain and phase leadcoefficients of Eq. 56 can be set, in a practical context, by empiricaldetermination of good performance, or they can be determined for aspecific control system from analytic considerations. Notice that in amicroprocessor that does not provide for fast numerical division, theratio “G/Φ_(tgt)” can be computed in advance of a solenoid launch andused as a constant multiplier during real-time dynamic control.

Concerning landing point errors, if the estimate used for “Φ_(tgt)” isin error, then either:

-   -   1) the position variable “x_(eff)” will exceed “x_(min)” as        velocity settles to zero, with no landing; or    -   2) the shuttle will land with a “bump” indicated by an abrupt        reduction or bounce in “dx_(eff)/dt.”

In case 1, as successive values of “Φ_(n+1)” approach a constant limit,that limit indicates the flux actually required to balance the loadforce, in which case the final value of flux may be set to the newtarget, “Φ_(tgt)” which will exceed the previous value.

In case 2, “Φ_(tgt)” has been overestimated and can be reduced by amultiplier slightly less than 1.0 for the next landing. Alternatively, abetter estimate of “Φ_(tgt)” might be computed if the controller is ableto observe and record values at the impact point. This computation couldbe tricky and dependent on the nature and nonlinearities of the specificcontroller apparatus. When premature landing takes place, thecontroller-determined dynamic flux “Φ_(n+1)” might be decreasing becauseof the increasing nonlinear multiplier (dx_(eff)/dx) of Eq. 42; or itmight be increasing since the shuttle is decelerating as it approachesits target, since that deceleration is decreasing toward zero, andtherefore since the force needed to hold the shuttle against the loadforce would be decreasing; or flux change on landing approach may bedriven significantly by changing load force. If there is any dynamicovershoot or tendency toward ringing in the control loop, this furthercomplicates determination of the soft landing target. In a practicalmethod, some reduction in target flux will be called for if the shuttlelands with a bump and is held at the mechanical stop. If there isbumping due to dynamic overshoot with final settling short of themechanical stop, this indicates a problem with the control loopparameters, which have been set for less than critical damping, callingfor adjustments in gain and phase lead to achieve the smoothest possibleapproach.

As a practical matter, there is generally “no hurry” about soft landing.When touchdown is approached, duty cycle and drive current are very low,so power consumption is near a minimum, whether or not actual mechanicalcontact is achieved in the solenoid. It is reasonable to contemplate acontroller design in which the target landing point is short of actualmechanical closure and the shuttle is caused to hover dynamically forthe duration of time that the solenoid is in an “energized” or “on”state. If hovering is maintained, the controller will effectively bemeasuring time-varying load force. For hovering performance, thecontroller might reasonably include a slowly-accumulating integralcorrection to error, which would track changing load and leave thecontroller initialized to recent load force history for the next launch.

The discussion above has concentrated entirely on controller operationapproaching a soft landing. At launch, Eq. 54 will generally dictate apulse interval t_(p), exceeding the time interval t, i.e. a duty cycleexceeding 100%. In this event, the controller will operate in a slewingmode. If control is based on AC determination of reciprocal inductancefrom current slope on a sawtooth waveform, or from ringing frequencyafter a voltage transition, then the system should slew at a pulseinterval set to give somewhat less than 100% duty cycle, so that therewill be an oscillation in current and a possibility of measuringreciprocal inductance dynamically. If control is based on integraldetermination of magnetic flux, then the driving amplifier can be turnedsteadily on until the controller method calls for a reduction in thepulse interval below its maximum. The launch phase must not establishsuch a high cumulative energy, including kinetic energy andinductively-stored energy, that the shuttle will overshoot its mark.There is the possibility of active “braking” of inductive current,including “regenerative braking” wherein excess inductive energy resultsin a pumping of charge back into the power supply. With active braking,a more aggressive launch is possible without overshoot, if the systemplaces any premium on actuation speed. In terms of energy conservation,experience has proved that as long as the drive voltage and windingimpedance are established such that the force on the shuttle overcomesthe load force by a reasonable margin, e.g., at least 125% of theminimum, and by not too large a margin, e.g., not in excess of 800% ofthe minimum, then the net energy dissipation will be quite close to theminimum achievable dissipation. A reasonable target is for an initialmagnetic force of about 200% of the minimum to produce accelerationagainst a spring preload, with design for a higher value where there isgreat uncertainty about the preload. In the case of a solenoid whoseshuttle starts out in equilibrium with a spring and encounters aprogressive increase in force as the magnetic gap closes, as a veryrough guideline, magnetic force should ramp up initially about twice asfast as the load force, i.e. a variation on the rule that magnetic forceshould be of the order of 200% of load force in the launch phase. If“reasonably” designed, the details of the controller method are notcritical to energy performance. The controller must establish launchwith a reasonable acceleration and must cut power soon enough to avoidovershoot of the landing target. The soft landing method outlinedmathematically above takes over from a launch-phase or slewing phase andis based on an exponential final approach to the target, which is arelatively simple method from a design standpoint. Other methods arepossible for providing non-exponential target approach paths, with aboutthe same overall energy performance.

Approximate Servo Control Methods

The above discussion has been directed toward a controller in which theposition variable “Xeff” is determined as a ratio, either ofcurrent/flux, or of d(current)/d(time)/d(flux)/d(time), the latter ratiobeing proportional to the reciprocal of dynamic inductance. Jayawant(U.S. Pat. No. 5,467,244) teaches a system for approximating the ratioof current/flux by a linear fit about an operating point. Consider theratio A/B of variables A and B, where A is close to A0 and B is close toB0. From the zero-order and linear terms of Taylor series expansions invariables A and B near A=A0 and B=B0, one obtains the linear ratioapproximation,A/B≅A0/B0+(A−A0)/B0−(B−B0)(A0/B0A^2) for A and B near constants A0 andB0.  57]

Since force obeys a square-law equation for solenoids, the followinglinear approximation (also from a Taylor expansion) is useful near aknown operating point, and is exploited by Jayawant:A ² ≅A0²+2(A)−A0)A0 for A near constant A0.  58]In both formulas, the perturbation differences A−A0 and B−B0 aremultiplied by fixed coefficients. When the operating point ispredetermined, as in the context described by Jayawant for magneticlevitation with small perturbations from the operating point, then alinear circuit can be used to implement the above quotient and ratioapproximations. For continuous levitation, however, there are problemswith Jayawant's approach of using the ratio I/Φ where the magnetic fluxΦ is determined as the time integral of an induced voltage:specifically, the integral drifts over time. An AC determination ofcurrent-change to flux-change is more cumbersome to implement byJayawant's approaches, requiring the use of a high-frequency carrier andamplitude detection. Furthermore, experience with real solenoids showsthat AC eddy currents induced in metal solenoid material cause themeasured inductance to deviate substantially from the idealrelationship, exploited by Jayawant, that 1/L indicates position X. Analternative approach offered here, employing I and Φ rather than theirderivatives, is to base control not entirely on estimated position, butrather on estimated force in the short term, and average actuationvoltage or current in the long term. If a solenoid is subject to astabilizing mechanical spring force as well as a destabilizing tendencyin the electromagnetic force, one can substantially reduce theelectromagnetic destabilization by exerting servo control for constantmagnetic flux, Φ, as determined by integration of induced voltage. Inthe short term, solenoid drive voltage is controlled by deviation offlux from a target flux value, which corresponds to a magnetic force inequilibrium with mechanical spring force at a desired final position. Tomaintain this position, a particular coil current will be required, andlong-term deviation of servo-controlled coil current from a target valueis taken as an indication that the integral estimate of magnetic flux isdrifting. Such drift is eliminated by summing into the flux integrator(or digital accumulator in a digital implementation of the controller)an error signal representing the difference between actual drive windingcurrent or voltage and that target current or voltage associated withthe desired position. In the long term, then, the controller stabilizescurrent or voltage to a target, which only works when the samecontroller is controlling current to stabilize magnetic flux in theshort term. Note that position measurement is absent from thisdescription. If the zero-velocity magnetic flux is on target, or if thelong-term average current needed to stabilize flux is on target, thenposition is on target by inference, based on a knowledge of the system.In a hybrid approach, short term servo control is based on a linearcombination of current and flux, as with Jayawant's linear ratioapproximation, but long-term control is based on average current oraverage applied coil voltage, which may in turn be estimated fromaverage pulse duty cycle from zero to a given supply voltage, in thecontext of a switching regulator. Implementation of this approach willbe described in an embodiment of the instant invention,

Jayawant's controllers employ linear power amplifiers to actuate thedrive coils, all approach which needlessly dissipates substantial power.A switching or Class-D amplifier can give an efficiency improvement, butthen the AC signals introduced into the controller circuit must be dealtwith. Taking advantage of that situation, embodiments described beloware designed intentionally to make the feedback loop go unstable andoscillate, by analogy to a thermostat that maintains a desiredtemperature within small error by switching its output discontinuouslyin response to measured error, resulting in a loop that controls dutycycle rather than a continuous analog parameter. This oscillatorycontrol loop approach results in an energy-conservative transformationfrom DC power at constant voltage into coil power at variable voltageand current. In an oscillatory control loop, AC signal information ispresent that can be used to advantage for servo control. One use of thisinformation parallels a use employed by Jayawant, where Jayawant appliesa known AC voltage amplitude to a coil at high frequency and reads theresulting AC current as a measure of reciprocal inductance and ofeffective magnetic gap. This approach by itself parallels applicant'suse, described under “OBJECTS OF THE INVENTION” as the numerator of thederivative difference ratio, of the quantity (dl/dt), the oscillatorychange in current slope. The instant invention, by contrast, derivesthis quantity from a very robust signal associated with powering thesolenoid, without an auxiliary oscillator. In the efficient switchingregulator environment taught here, switching noise at constantly varyingfrequency and duty cycle would mask a small carrier signal such as istaught by Jayawant, but in the new context, the switching noise itselfis interpreted as a position-indicating signal. As will be shown,one-sided rectification of switching noise induced in a sense coil canbe used to infer solenoid current from a large, robust signal, withoutreliance on extraction of current information from a current senseresistor, whose voltage differential signal must in the simplest drivertopologies be read against a large common-mode voltage swing.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS LAUNCH CONTROL METHODS

We have discussed the achievement of linear servo control, whose outcomeis to establish a roughly exponential decay of error, including simpleexponential decay and ringing within a decaying exponential envelope. Areal solenoid controller has built-in slew rate limits that setboundaries to the region of linear behavior and, consequently, the rangeof applicability of linear control methods. Typically, the solenoiddriver amplifier operates between voltage output limits that set themaximum rate at which solenoid current can be increased and decreased.In the most common two-state output controller, the “on” output statedrives current toward a maximum while the “off” output stateshort-circuits the solenoid winding through a transistor, allowing thecurrent to vary and, ultimately, decay, in passive response toresistance and changing magnetic gap. The momentum attained by thesolenoid shuttle falls into two categories: mechanical andelectromagnetic. The mechanical momentum is related to the inertia ofthe solenoid shuttle and its coupled load. The “electromagneticmomentum” is the natural persistence of the solenoid magnetic field. Acontroller can be designed to provide braking of electromagneticmomentum if it provides a drive output state that resists the flow ofelectric current in the solenoid drive winding. A switching controllercan provide an output state designated “brake” that slows the flow ofcurrent established during the “on” state faster than that flow wouldslow down in the “off” state. An effective way to provide a “brake”state in a two-transistor output stage, one transistor connecting theoutput to a supply voltage and the other transistor connecting theoutput to a ground voltage, is to “tri-state” the output, i.e. to turnboth transistors off, and provide a zener clamp diode between the outputand ground to limit the inductively-produced voltage swing on the farside of ground potential from the DC supply potential (i.e. a negativeswing for a positive supply or a positive swing for a negative supply).A more complicated “H” drive output configuration, familiar toelectrical engineers, functions with a double-pole double-throw-switchto reverse the solenoid lead connections and allow the inductive current“momentum” of the solenoid to pump current back into the single supplyrail in the “regenerative braking” mode mentioned earlier. Notice thatregenerative braking can only reduce the electromagnetic “momentum”quickly, removing but not reversing the electromagnetic driving force.This is because electromagnetic force is a solenoid not base donpermanent magnets is inherently unipolar, a square law phenomenon, asindicated, e.g., in Eq. 42, whose only controlled term is the square-lawterm “Φ².” The variable multiplier term “dx_(eff)/dx” of Eq. 42 is afunction only of position “x_(eff)” and cannot be altered or reversed bythe controller. Thus, even with electrical braking, there is no quickway to brake the mechanical momentum toward closure of a magnetic gap.Thus, one is inevitably confronted with a mechanical slewing limitationand the inevitably of overshoot if one establishes an excessive momentumtoward gap closure. For providing soft landing at full-open, the slewrate limit imposed by a finite supply rail voltage implies an upperlimit to electromagnetic braking of a shuttle driven by mechanicalsprings. Again, this situation implies that when excessive momentum isestablished toward the full-open limit stop, overshoot and impact areinevitable.

Where the direction of momentum is specified, i.e., toward full-closureor full-open position, then it is useful to analyze slewing dynamics interms of energy rather than momentum. Whereas the definitions ofmechanical and electromagnetic “momentum” differ, energy is commonlydescribed by the same units (e.g., joules in S.I. units) in bothmechanical and electromagnetic contexts, and it is meaningful to speakof the total energy of the solenoid, combining mechanical andelectromagnetic terms. At full closure with zero velocity for a solenoidshuttle being pushed open by a mechanical spring, the total energy ofthe solenoid assembly is the potential energy of the spring. Whileanalysis is possible for any specific nonlinear spring or complexmechanical load including masses, nonlinear springs, and nonlineardampers, we will restrict ourselves here to the commonplace and usefulexample of a linear spring and a single lumped mass, described by Eq. 36as repeated here:d ² x/dt ²=(F+K 1(x ₁ −x))/M acceleration equation repeated here  36]

To review, the mechanical spring rate is “K1,” and “x₁” describes thecoordinate of a fully relaxed spring. The full-open mechanical stop forthis system, defined by x=x_(open), will lie between x=0 and x=x₁ for asystem with a spring preload. Eq. 36 is valid only for the range between0 and x₁, i.e. between the mechanical stops defining full-close andfull-open. The mechanical potential energy of this system varies betweenminimum and maximum limits: $\begin{matrix}{E_{p.\max} = {\frac{1}{2}{{K1} \cdot x_{1}^{2}}\quad{maximum}\quad{potential}\quad{energy}}} & \left. 59 \right\rbrack \\{E_{p.\min} = {\frac{1}{2}{{K1} \cdot \left( {x_{1} - x_{open}} \right)^{2}}\quad{minimum}\quad{potential}\quad{energy}}} & \left. 60 \right\rbrack\end{matrix}$

In the simplest control situation, all the constants of Eqs. 36, 59, and60 are known in advance and can be incorporated into a control methodfor a specific solenoid. In interesting situations, one or morecharacteristics of the mechanical load of the solenoid will be unknownat the time of solenoid launch. In a practical solenoid applicationdescribed later in this paper, the effective total mass “M” and thespring constant “K1” do not vary, but conditions at launch do vary.Specifically, the solenoid pulls on a short-stroke piston (describedlater, using a molded plastic “living hinge” or rolling seal rather thana sliding fluid seal) that draws a fluid through a valve, which remainsclosed before launch time. The pressure of the fluid behind that closedvalve is unknown at launch, which amounts to not knowing the forcepreload on the system and, consequently, the equilibrium value of “x₁.”When the solenoid is energized and begins to move, and specifically whenits motion is coupled to the source fluid pressure through an openvalve, then the acceleration of the shuttle is an indication of theeffective preload. Analysis of measurements taken early in launch leadto a determination of the launch pulse duration needed to generate atrajectory toward a specific target value “x_(tgt)” at the minimum pointof the trajectory. The starting value of “x,” which is “x_(open)” in Eq.60, will vary according to the initial fluid volume behind the piston.The value of “x_(tgt)” will also vary according to the desired finalfluid volume behind the piston. At maximum fill, x_(tgt)=0, i.e., thesolenoid reaches maximum magnetic closure, but in typical operation theend-point volume is targeted as less than maximum fill. In this solenoidcontrol context, there is no use of “soft landing” or servo-controlledconvergence to a target “x.” In one configuration, passive fluid checkvalves halt the motion of both the fluid and the magnetic shuttle up tolaunch time and after the shuttle passes its position of maximum closureand begins to fall back toward open. In an alternate configuration,active solenoid valves perform similar functions to check valves butpermit more flexible control, particularly for precision dispensing offluid in medical infusions and industrial applications. It is seen thatin the context just described, the entirety of solenoid servo controlconsists of launch control to achieve a prescribed target under variableoperating conditions, with no use of soft-landing control.

Controller designs and methods meeting the requirements of this pumpingapplication are applicable in more restrictive contexts, e.g., where thefull-open start position for the solenoid is fixed but the spring biasresisting solenoid closure to a specified “x_(tgt)” is unknown until thesolenoid lifts away from its full-open stop. Common applications willcall for an adaptive launch method combined with a soft-landing methodthat takes over the final part of the solenoid trajectory, once unwantedpreconditions for overshoot have been avoided by the launch method. Thenonlinear adaptive launch method to be described below can give aminimum-time trajectory to a target. It is feasible to dispense withseparate launch control and use a linear “soft-landing” method fromlaunch onward, provided that the phase-lead time constant “τ” (Eq. 56)is made large enough to bring the system out of slewing before too muchenergy has been injected. To achieve maximum speed, the value of “τ”would have to vary according to launch conditions that may be unknown inadvance. Maximum speed, however, will often be of little practicalimportance.

Of greater importance in the fluid pump application described above isthe freeing of a microprocessor from a solenoid control task to make wayfor another task. Specifically, the active valve pump embodiment to bedescribed later involves three controlled solenoids, one for pistonpumping and two for valve actuation. For economy, all three valves canbe made to operate from a single microprocessor controller. The pistonsolenoid is energized first, to full-on, after which a regular timesequence of samples from a sense winding provide values proportional to“dΦ/dt,” the rate of change of magnetic flux. A running total of theseregular samples gives the present flux. Interleaved with sampling andsumming of samples of “dΦ/dt” the microprocessor controls the inletfluid valve solenoid to reach full-open with a soft landing and switchto a low-computation holding mode, e.g., at a predetermined holding dutycycle. The controller then returns its attention to the piston solenoidto determine a cutoff time for achievement of a prescribed “x_(tgt).”Once that cutoff time is reached and the piston solenoid is shut down,the controller can wait for the projected trajectory interval to elapseand then shut down the inlet valve. At this point, the pumped volume hasbeen captured, and the computation tasks relating to the solenoids forthe inlet valve and piston are done. The microprocessor can thereforeconcentrate on the tasks of pulsing the outlet valve and dispensing thefluid that has been pulled in by the piston.

To summarize the method development task ahead, we seek a launchcontroller that begins launch with an initially unknown effectivespring-balance value “x₁” whose physical location is beyond thefull-open mechanical stop at x_(open) (i.e., the spring preloads theshuttle against a full-open stop) and which adaptively targets apredetermined but possibly variable minimum value of“x” at “x_(tgt)”where the shuttle velocity goes through zero. The value of “x_(tgt)” maybe set at or just barely above zero where a simple soft landing issought, such that the solenoid shuttle stops in the vicinity of fullclosure, possibly with a minor bump, and is then pulled to full closure,with a first or possibly second minor bump, using a few open-loop powerpulses of appropriate magnitude.

The specific procedure given below suggests the manner of approachingdifferent but related control problems that will arise in practicalsituations. A generalized mathematical treatment for control underunknown mechanical conditions would be quite difficult to approach,given the multitude of ways in which practical systems can differ. Theanalysis below, following relatively quickly from the governingequations given above, represents but one of many variant paths from thegoverning equations to a control method appropriate for a specificapplication. With the example to be given, the engineer skilled in theart in this area of control engineering, and schooled in the form ofanalysis provided in detail in this disclosure, will be able to come upwith a control method and/or controller design tailored to theparticular application, but falling within the scope of the inventionbeing disclosed herein.

In the event that “x_(open)” from Eq. 60 is not initially known to acontroller or control algorithm, this value may be measured with a lowlevel power pulse that causes little or no solenoid motion and thatconsumes little energy. Starting at zero current and zero flux, afixed-duration voltage pulse is applied. Sense winding readings aretaken at regular intervals and summed to a register to provide anintegrating variable proportional to the total magnetic flux, “Φ.”Alternatively, where no separate sense winding is provided, current “I”is measured and a computed “I·R” voltage drop across the winding issubtracted from the voltage applied to the winding to infer the inducedvoltage in the drive coil, which in turn is integrated over multiplesamples to provide a running estimate of flux “Φ.” In the vicinity ofthe end of this pulse, perhaps both before and after the end of thepulse, electric current “I” flowing through the drive winding is dividedby flux “Φ” to compute “x_(eff)” from Eq. 38. As has been shown,“x_(eff)” can also be determined from current slopes at differing drivevoltages using Eq. 40, inferring reciprocal inductance “1/L” fromcurrent slopes. It is seen that for a single pulse, computing “1/L” fromcurrent slopes and correcting for the effect of electrical resistanceamounts to the same thing as computing flux “Φ” fromresistance-corrected coil voltage and cumulative current. It is only inthe redetermination of “x_(eff)” during later voltage pulses that theflux and reciprocal-inductance methods differ. This position parameterthus obtained is used to compute-“x(_(open),” e.g., by inversion ofapproximate curve-fit Eq. 20 to solve for “x=x_(open)” from “x_(eff).”The pulse width used for this determination is chosen small enough thatthe solenoid force does not overcome the preload force and there is nomotion. For convenience, current and flux are allowed to settle toessentially zero before the launch pulse.

By an alternative approach, the initial or open value of “x_(eff)” isdetermined by connecting a capacitor across the solenoid coil, measuringa resonant frequency or period, and computing inductance L or itsreciprocal, I/L. A first preferred embodiment of the invention includesa “ping” circuit for gap determination, although that embodiment is aservomechanism rather than a launch control apparatus.

Having determined “x_(open)” the controller now initiates the voltagepulse to the drive solenoid. Current will ramp up at a rate limited byinductance until the magnetic force is sufficient to overcome the springpreload and start the shuttle moving. Before shuttle motion begins,theory predicts that current “I” will increase in linear proportion toflux “Φ” in the ratio that was already measured to determine “x_(open).”Empirical measurement has shown that with ferrite solenoid components,this linear proportion is observed in measurement to good accuracy. Assoon as the magnetic gap begins to close, the ratio “I/Φ” will begin todecrease. If the excitation is not a continuous pulse but a pulse trainat high duty cycle, so that current ripple can be measured to determinereciprocal inductance, “I/L,” then this measure of magnetic gap willalso hold steady until the magnetic force exceeds (tic preload forcethreshold and the gap begins to shrink. Let us suppose that a thresholdis set for detection of shuttle motion, specifically when “x_(eff)” isreduced fractionally by “ε” below the value corresponding to thelinearized distance parameter “x_(open).” In terms of repeatedmeasurements of “I” and integrated “Φ” this reduction is expressed bythe threshold inequality of Eq. 61, which derives from Eq. 38:I<(I−ε)(I _(open)/Φ_(open))(Φ) current/flux threshold equation formotion detection  61]

The values for “I_(open)” and “Φ_(open)” are the numbers that were used,in the pre-launch pulse test, to compute “x_(open),” and the reference(I_(open)/Φ_(open)) ratio of Eq. 61 is pre-computed, appearing as aconstant during the rapid repetitive computations to detect a thresholdcrossing. To avoid repeated division computations, the time-varying fluxdenominator “Φ” of Eq. 38 is multiplied through to yield the form of Eq.61, free of repetitive division computations.

If the launch on-pulse is interrupted by short off-pulses to reveal thechanging AC impedance of the coil, an AC equivalent of Eq. 61 is derivedfrom Eq. 39 and expressed in Eq. 62:(dI/dt)<(l−ε)(Δ(dI/dt)open) current slope threshold equation for motiondetection  62]

In getting from Eq. 39 to Eq. 62, it is assumed that the denominatorvoltage change V is constant, being primarily the power supply voltagebut with corrections, e.g., for the forward drop of acurrent-recirculating diode. The change in current slope is associatedwith the switching transition of the driver transistor, e.g. transistor509 of FIG. 5, which will be examined later. The constant“(dI/dt)_(open)” on the right of Eq. 62 is the value that was used, inthe pre-launch pulse test, to define “x_(open)” By keeping thedenominator interval “dt” fixed, the change in current slope istransformed into a simple second-difference among three equally-spacedcurrent samples. Thus, the left side of Eq. 62 becomes a seconddifference among samples, while the right side is a constant.

The threshold value for “ε” may be set at a low, practical value, e.g.,ε=0.05, so that a combination of circuit noise, quantization error, andarithmetic error will not cause a false trigger. The time delay from thestart of the launch pulse to passage of the motion threshold associatedwith a given “ε,” as determined by the first measurement that satisfiesEq. 61 or 62, is designated simply t_(ε).

If one could extrapolate back from the triggering event at t_(ε), to theestimated current where the force balance threshold was crossed, thenone could quantify the preload force and, from there, define all theanalytic parameters that determine shuttle trajectory as a function ofthe electrical input. For the pragmatic task of launching the solenoidon a trajectory to a desired maximum closure at x=x_(tgt), however,analytic solutions are quite cumbersome, and an empirically derivedfunction is quite sufficient for launch control. In the contextpresented, this function has three arguments:

-   -   Xopen=launch start point, measured via pre-launch pulse and Eq.        38 or 40 and 20a    -   Xtgt=target end point, measurable by a test pulse at the        trajectory end    -   tε=launch acceleration time for motion to designated fraction of        full trajectory

Based on these three arguments, one desires a launch pulse period,t_(p), that will cause a trajectory to reach the target:t _(p) =t _(p)(x _(open) , x _(tgt) , t _(ε) defines arguments of pulseperiod function  63]

The nature of this pulse of width t_(p) is better understood in light ofFIG. 1, which illustrates the waveforms associated with the launch of asolenoid whose magnetic closure force must exceed a mechanical preloadforce before motion begins. The coil drive voltage Vd is zero up totime=0, at the left edge of the family of traces and the beginning oftrace 110, at which point Vd goes high for a pulse interval extending to115, where trace 110 returns to its low state and the drive pulseinterval terminates. Current 1, trace 120, begins to rise starting fromthe left-hand end, causing an increasing force varying as the square ofI. When this force exceeds the mechanical preload, then velocity trace130, dX/dt, labeled {dot over (X)} where the dot above the letterdesignates time differentiation, begins a negative excursion from zero,indicating that gap X is becoming smaller. Trace 140 illustrates theintegral of dX/dt, which is gap X. Trace 150 illustrates the inducedvoltage Vi, which has the effect of limiting the rate of increase ofcurrent I in the drive winding, and which may be detected free fromother signals in a sense winding wound coaxial with the drive winding.Where current is zero at the left-hand edge, Vi initially equals thesupply voltage. Essentially the same Vi signal may be obtained from asense winding, though the sense voltage will be multiplied by the ratioof sense winding turns to drive winding turns. Before motion begins anddX/dt departs from zero, current I along trace 120 follows anexponential decay upward toward an asymptote where ohmic resistivevoltage balances the supply voltage, while Vi along trace 150 follows anexponential decay downward toward an asymptote at zero. Motion beginswhen the solenoid shuttle lifts off its mechanical stop, or in a contextto be described later, when the pull of a solenoid-driven piston reducesthe pressure in a fluid chamber below a source pressure, causing aone-way check valve to open. The resulting fluid flow allows the pistonand solenoid shuttle to begin moving. The closing of gap X toward zeroreduces and then reverses the-upward slope of current 1, causing trace120 to fall below the exponential path that it followed initially. Asthe current increase is halted, the decline in induced voltage Vi ontrace 150 is halted. Shortly beyond these zero-slope points, at the timeof Vd transition 115, the applied coil voltage is removed and the drivecoil is short-circuited, allowing current flow to continue as sustainedby inductance. The induced voltage goes in a downward step from thepositive value: (supply-voltage−I*R) to the negative value: (−I*R), fromwhich point trace 150 decays upward toward a zero asymptote. Current isdriven toward zero by a combination of resistive voltage and magneticgap closure, with gap closure coming to dominate over resistance in thedetermination of current as the gap becomes small. As trace 140 and gapX reach a minimum, with dX/dt reaching zero, a fluid check valve closes,preventing reverse flow and preventing a subsequent increase in gap X.Through a correct adjustment of the pulse width on Vd, the final valueof gap X is reduced to 10% of its starting value. The present discussioncenters on a determination of the pulse width t_(p) that will cause this90% gap reduction to take place.

If the pulse interval is increased by about 3%, the 10% gap residualwill be reduced to 0%. FIG. 2 illustrates the result of a 5% increase inthe pulse interval, where the off transition time of trace 210 at 215 isdelayed 5% later than at 115 of FIG. 1. It is seen that dX/dt, labeledas {dot over (X)}, along trace 230 goes more negative than for trace130, and X along trace 240 reaches zero at 245, indicating the point ofimpact. At this time, dX/dt trace 230 jumps to zero at 235, indicatingthat the solenoid shuttle is brought to an abrupt halt. The simulationprogram generating these traces includes an idealized fluid check valvethat completely prevents rebound in X, whereas a comparable empiricalset of traces would show effects of rebound and subsequent settlingbounces. When gap X is stopped at zero at 245, current I along trace 220is driven nearly to zero at 225. Induced voltage Vi along trace 250reaches nearly to zero when X reaches zero.

FIG. 3 illustrates the result of a 5% decrease in the pulse interval oftrace 310 to transition 315, as compared to the baseline transition oftrace 115. The decrease in gap X along trace 340 terminates earlier andat a substantially higher end value, where motion is terminated by checkvalve closure. Trace 330, indicating dX/dt, labeled as {dot over (X)},exhibits a negative peak and a return to zero, while trace 320,indicating current I, continues to decay after motion in X has stopped,as Indicated by the return of trace 330 to zero. Trace 350, illustratinginduced voltage Vi, exhibits a similar decay toward zero from below andextending beyond the point where shuttle motion stops. Comparing currentdecay traces 120 and 320, the decay time constant for trace 320 isshorter (giving faster settling) than for trace 120. Both decays areexponential with a time constant of −L/R, where R is circuit resistanceincluding coil resistance and L is solenoid inductance. Inductance L islarger for FIG. 1 and trace 120 because of the smaller gap X achievedalong trace 140, as compared to trace 340, thus explaining the fastersettling time constant for trace 320.

Returning to Eq. 63, we have postulated an advance measurement ofx_(open) and a predetermined value of x_(tgt), leaving only one unknown,t_(ε), to be determined “on-the-fly.” The event that sets t, is positionX crossing a threshold indicating that motion has begun, where thischange in X is inferred from a change in the ratio of current/fluxaccording to Eq. 61. A change in the ratio of derivatives,(d(current)/d(time))/(d(flux)/d(time)), performs equivalently fordetecting a position change, and detection of such a change issimplified to solution of the threshold inequality Eq. 62. Using eitherEq. 61 or Eq. 62, the intent is to detect incipient solenoid motion,and, by the timing of this detection, to define a future time at which alaunch power pulse should terminate. An unknown preload condition willcause the timing to vary. FIGS. 1, 2, and 3 indicated sensitivity of gapclosure to pulse interval under fixed preload conditions. FIG. 4illustrates traces for differing preload forces and the use of threedistinct methods to determine a launch pulse interval dynamically,on-the-fly. First we consider FIG. 4 illustrating the results ofimplementing Eq. 63 in a controller that sets x_(tgt) to 10% of x_(open)and solves for t_(ε) to achieve this final gap, which is indicated attrace 447, where three X traces converge to a single line. The systembeing simulated for FIG. 4 is a pump whose piston is driven directly bya solenoid. The variable preload is a variable fluid pressure at theinlet of the pump, behind a one-way check valve. With the check valveclosed, the solenoid driver system has no way to sense the unknownpressure that will affect the launch. When the drive signal Vd goeshigh, causing voltage to be applied to the solenoid drive winding,current I will build up for a period of time before enough force isachieved to open the check valve and allow solenoid motion to begin. Ata positive pressure, e.g., +3 psi, the check valve is alreadyforward-biased, and a very small magnetic force unsticks the valve,initiating the almost immediate acceleration observed in thefastest-descending trace 432 of dX/dt (labeled X) and, observableslightly later, a decline in trace 442 of X, which crosses fixedthreshold trace 440 where the line from the label “442” touches thetrace. This position threshold crossing is detected indirectly viaeither Eq. 61 or Eq. 62, as was explained above. The constant value oftrace 440 correlates with the threshold parameter ε of Eqs. 61 and 62.At a more negative pressure, e.g., 0 psi, the solenoid must develop alarger magnetic force before overcoming the fluid force bias andinitiating shuttle motion, as indicated in the velocity domain by trace434 and in the position domain by trace 444. Trace 444 crosses thresholdtrace 440 at the tip of the line from the label “444.” At a still morenegative pressure, e.g., −3 psi, the solenoid must develop a stilllarger magnetic force before overcoming the fluid force bias andinitiating shuttle motion, as indicated in the velocity domain by trace436 and in the position domain by trace 446. Trace 446 crosses thresholdtrace 440 at the tip of the line from the label “446.” Thus, threethreshold-crossing time points are defined by the three fluid pressures.For the threshold times associated with 442, 444, and 446, there aretarget switch-off times defined by the Vd transitions at 412, 414, and416. The threshold times define values for t_(ε) in Eq. 63, and theswitch-off times define the computed pulse widths t_(p). The threevelocity and position traces just described for increasingly negativeinlet pressures correspond to traces of currents 422, 424, and 426 andinduced voltages 452, 454, and 456. For reference, trace numbers endingin the digit “8” correspond to no solenoid motion at all, leading to nodownward transition of Vd trace 418, an exponential decay of currenttrace 428 to a resistance-limited maximum, zero-velocity trace 438,fixed position trace 448, and a simple exponential decay of inducedvoltage trace 458 toward zero.

An obvious method of defining the specific numerical values for Eq. 63is a combination of empirical measurement and mathematical curvefitting. One begins with an instrumented prototype of the system to bemanufactured and controlled. One sets an input bias, e.g., a bias fluidpressure, and experimentally pulses the system until an interval isdetermined that carries the solenoid from a specified starting positionto a specified final position. The determined time intervals arerecorded and the test repeated for other input bias values. Theresulting data sets define Eq. 63 for a specified, fixed initialposition and a specified, fixed final position. A one-dimensional curvefit to the data is obtained and programmed into a controller.

If the controller is to be operated with variable initial positions,then the parameter x_(open) of Eq. 63 comes into play, raising thedimensionality of Eq. 63 from one to two. Conceptually, one must nowrepeat the series of experiments described in the previous paragraph fora series of different starting values x_(open) yielding a family ofcurves. The specific computation algorithm used to implement Eq. 63 mustthen be capable of defining a specific member of the family of curveswhen the starting value x_(open) is specified. In actual hardware,x_(open) is a measurement, a reading taken in advance of launch. As willbe shown in hardware embodiments, the parameter used in place ofx_(open) is not a true magnetic gap, but rather a measurable electricalparameter of the solenoid corresponding to the magnetic gap, e.g.,inductance, or ringing frequency of the solenoid in a tuned circuit witha capacitor.

If the parameter x_(open) is fixed but x_(tgt) is to be made variable,then the situation is comparable to that of the last paragraph, with Eq.63 defining a two-dimensional surface, to be regarded as a family ofone-dimensional curves, one of which is to be preselected when x_(tgt)is defined.

For defining interpolation over a smooth surface defined by Eq. 63 whentwo input parameters are free to vary, one approach is multinomial curvefitting. Multinomial become cumbersome even in two domain variables, andmuch more so in three domain variables, due to the proliferation ofcross-product terms at high orders. Interpolation from a two- orthree-dimensional table is a relatively easy method for implementing Eq.63. A hybrid of table interpolation and polynomial curve fitting is toexpress each coefficient of a polynomial in the variable “t_(p)” interms of a tabular interpolation with respect the variable x_(open) orx_(tgt) or, in the general case, in terms of the variable pair(x_(open), x_(tgt)). The particular values for x_(open) and x_(tgt) willbe established before launch, and using those values, each of theseveral polynomial coefficients is defined by an interpolation. The setof coefficients thus obtained defines a specific polynomialt_(p)=POLY(t_(ε)) for use in the real time computation, immediatelyafter “t_(ε)” is measured and before the interval defining “t_(p)” haselapsed.

For any of the launch control situations described above, computersimulation may be used at least for a preliminary computationaldefinition of Eq. 63. A curve-fit method derived from computersimulations can be used for designing and evaluating the overallactuation system, including determination of the system's complexity,cost, efficiency, and sensitivity of control to resolution of time andparameter measurements, including the needed bit resolution for analogconversions. Once a system has been computer-designed and built inhardware, the specific parameters for implementation of Eq. 63 may befine-tuned using empirical data, which will generally be subject tophysical phenomena not fully modeled in the computer (e.g., to theviscoelastic properties of a rubber pump diaphragm, which are difficultto predict from a simulation)

Examining potentially simpler methods that accomplish the same purposeas Eq. 63, consider curve 420 of FIG. 4, which defines all empiricalthreshold function for current I. In the case where the solenoid shuttleis held fixed, current follows exponential curve 428 to aconstant-current asymptote. Shuttle motion generates an increasedinduced voltage, opposing current, that causes the curve of current withtime to bend downward from trace 428. Through measurement or computersimulation, one determines the transition times, e.g., for transitions412, 414, and 416, of drive control voltage Vd, that under variablepreload conditions result in the desired ending values of X, e.g., atthe value of 440. From these observations, one records the values ofcurrent I at the moment of transition of Vd, e.g., at 422, 424, and 426,corresponding respectively to the transition times of 412, 414, and 416.Plotting the values of 422, 424, and 426 on a time chart andinterpolating a smooth curve yields a threshold function for current I,e.g. trace 420. In controller operation, then, samples of current I aredigitally converted in rapid sequence and compared to corresponding timevalues from a table describing trace 420. When a current sample isobserved to fall below the threshold function, the controllerimmediately switches control voltage Vd to its low state, terminatingthe launch pulse. There is no need, as in Eqs. 61 or 62, to defineshuttle position, since any parameter indicating a change in shuttleposition and describing a well-behaved threshold function will suffice.If the threshold function is allowed to be a curve rather than aconstant value, then the pulse termination time can be made “now,” i.e.immediately after threshold detection, rather than some functiondescribing additional time delay. Simplicity of one constant function istraded off against the complexity of another variable function.

By similar reasoning to the above paragraph, a threshold function can bedescribed in relation to induced voltage Vi, instead of current 1. Thisthreshold function is illustrated by trace 450, which touches the Vicurves at 452, 454, and 456, defining the transition times for 412, 414,and 416, respectively. Observe that the triggering of Vd causes the Vicurve immediately to break away from the threshold curve 450, whereascurrent triggering at trace 420 caused the current curves to bend downacross the threshold function.

Other threshold functions are readily derived. Consider the example of athreshold function that incorporates the exponential nature of theno-motion induced velocity trace 458. An exponential function f decayingtoward zero with time constant τ takes the general form f=A EXP)(−t/τ).The time derivative is then df/dt=−(A/τ)·EXP(−t/τ). The weighted sumgiven by “f+τ·df/dt” is particularly useful as a threshold function,since this sum equals zero up to the moment when X begins to change.Hence, this particular sum is an especially sensitive indicator ofmotion and amenable to motion threshold detection in a real device. Tocomplicate the use of this threshold function, the time constant τ isnot constant with operating conditions, but varies in proportion toinitial solenoid inductance, which in turn depends on the parameterx_(open).

It is noted that the threshold reference function to which (e.g.) thesum “f+τ·df/dt” is compared is a slice of a higher-dimensional function,that slice being cut at a value of x_(open). Thus, the significantparameters for threshold detection are all altered by initial solenoidposition for the approach described in this paragraph.

To implement the strategies illustrated in FIG. 4, FIG. 5 illustratesinterface circuitry between a control computer and a solenoid, includingdriver and sensor electronics. The electromechanical and magnetic systemto be controlled is drawn above 500 as a hybrid of a transformer symboland the shape of a “U-I” magnetic core pair with a gap, the “U” at 501opening to the left and the “I” at 502 as a rectangular piece cappingthe “U” with a variable gap, “X” at 503. A mechanical suspensiondefining a mechanical impedance of the “I” shuttle piece with respect tothe “U” stator is shown as the spring symbol 504 and the dashpot ordamper symbol 505, connected between the “U” and “I” such that each seesthe entire relative motion of the two pieces and each contributes itsforce additively to affect rate of change of spacing. An inertia of themechanical system is assumed, though not drawn explicitly, being partlyinertia of the solenoid shuttle and partly inertia of the load. A realmechanical of fluid-mechanical load will, in general, be morecomplicated than the load diagrammed. Not diagrammed is some mechanismfor enforcing linear motion without rotation of shuttle 502 with respectto stator 501, such that the two magnetic gaps are forced to remainsubstantially equal except very near closure, where even a very smallmechanical alignment error results in one side closing before the other.It is noted that in any shape of electromagnetic core, and in someshapes much more than others, there is a strong magnetic/mechanicaldestabilizing force favoring unequal closure of magnetic gaps. Simplystated, magnetic flux concentrates wherever a gap is narrower, and thisconcentration leads to an increase in attractive force, driving thenarrowest part of the magnetic gap toward further closure.

The solenoid windings, including the drive winding 506 and the sensewinding 507, actually wrap around the core, sharing substantially thesame magnetic flux, but they are diagrammed as is conventional withtransformers, as helices running alongside the part of the diagramrepresenting the magnetic core. The polarity convention is that when avoltage appears +to − from the top to the bottom of one coil, the sameinduced potential will appear in the other coil terminals, going +to −from top to bottom. From a physicist's standpoint, the coils areintended to spiral with the same sense (i.e. clockwise orcounterclockwise) going from top to bottom, with the result that thesigns of d(flux)/d(time) in the two coils match and yield inducedvoltages of like sign and with potentials in the same ratio as thenumbers of windings. Thus, when a positive voltage from V, at 528 isapplied, via series current sense resistor 524, to node 526 includingthe upper terminal of winding 506, and the circuit is completed via thelower terminal of 506 at 508 into the drain of N-channel enhancementmode field effect transistor (FET) 509, and thence via the source node511 into ground terminal 514, and when FET 509 is turned on, then thepositive-to-negative potential difference from top to bottom of 506 willdrive current down through the coil. The rate of increase of thiscurrent will be opposed by an induced voltage, which will appear in thesame direction in 507, tending to cause a current flow from bottom totop of that coil, i.e. in a direction that would oppose the externalpotential applied to the bottom coil. Recalling the gedanken experimentswith superconducting coils as used to derive the early electromagneticformulas, were there no resistance in the secondary coil, and were thatcoil shorted, then the ampere-turns of current flow in the secondarycoil would cancel the ampere-turns in the primary, meaning that thecurrents would tend to flow in opposite directions, the one drivenexternally against the induced potential, the other driven from withinand in the direction of the induced potential.

Coil 507 is grounded at its lower terminal and connects via node 532 tothe non-inverting input of unity buffer amplifier 550, whose output node534 connects back to the inverting input of 550. 534 also connects intothe channel 0, or “ch0” input of Analog/Digital Converter (ADC) 540,whose output connects via bus 542 to computer (CPU) 520. Thus, 520receives digital data indicating the induced voltage in coil 507, whichvaries in known proportion to the induced voltage in 506. The inducedvoltage signal is proportional to the rate of change of magnetic fluxthrough the windings 506 and 507. As stated in the mathematical sectionabove, the induced voltage signal to the CPU via 534 and channel 0 isalso a transformed potential representing the sum of the applied voltageand the resistive voltage: recall Eq. 50 for the voltage transformerrelation, and Eq. 51 for an expression in terms of rate of change ofmagnetic flux. Since buffer amplifier 550 draws negligible current via532, the voltage appearing at 532 from coil 507 lacks a significantresistive term and therefore indicates only V₁, the induced or inductivecomponent of voltage. Completing the diagram of FIG. 5, a CPU digitaloutput line at node 512 connects to the gate of FET 509, controlling theon/off switching of that FET with the respective high/low switching of512. When 509 is off and current is established flowing down through506, the current can complete a loop from 508 upward via the anode ofshottky diode 510 to the cathode connecting to node 522, which alsoconnects to positive power supply 528 and to the non-inverting “+A”input of instrumentation amplifier 530. The inverting “−A” input ofinstrumentation amplifier 530 receives its potential from node 526,which includes the bottom of current sense resistor 524 and the top ofcoil 506. The instrumentation amplifier has a well-controlleddifferential voltage gain of “A” as indicated by the “+−A” and “−A”labeling on its inputs, while the amplifier common mode gain isextremely low. The output of 530 at node 536 connects of channel 1 or“ch1” input of ADC 540, where the input signal is converted to digitalrepresentation and sent via bus 542 to the CPU. The signal thusconverted from 536 indicates the current flowing through sense resistor524, which equals the current flowing through 506 excepting for anegligible current into the inverting input of 530.

Given the computer and interface circuit or FIG. 5, with appropriatesoftware and adequate speed and timing capability, computer 520 canimplement the launch control methods described in relation to the tracesof FIG. 4. Using both channel 0 and channel 1 inputs, i.e. inducedvoltage and current, the computer can integrate (by a running numericalsummation) induced voltage to get flux, and can ratio current to flux toobtain a position estimate, and can then implement the thresholddetection and pulse interval determination of Eq. 63. Alternatively,using only the induced voltage signal at channel 0, the computer canimplement the threshold detection on induced voltage described by trace450. Or, using only the current signal at channel 1, the computer canimplement the threshold detection of current described by trace 420. Todetect initial gap “X” the computer can output a probe pulse and computea subsequent ratio of current/flux based on the perturbations observedin channels 0 and 1, all at a current insufficient to move the solenoidshuttle from its mechanical stop. Thus, the initial gap x_(open) can beinferred in preparation for launch control. A user interface or hostcomputer interface, not shown in the diagrams, can be used to receivecommands regarding variation in the target gap, x_(tgt).

A Noonolinear Continuous Servo Controller

Launch control methods and devices are limited in their scope ofoperation to situations where initial conditions are stable andmeasurable and where control extends only to a simple trajectory from astarting position to a target. Continuous control is more complicatedbut much more flexible, allowing for a system about which less is knownin advance and, obviously, allowing continuing control, for gap closure,gap opening, and levitation. FIG. 6 illustrates a continuous analogcontroller using multiplication and division to derive force and motionparameters for a conventional Proportional-Integral-Derivative, or PID,controller. The solenoid at 500 and the associated circuitry fordetecting current and induced voltage are the same as in FIG. 5, socomponents already explained in reference to FIG. 5 are unlabeled inFIG. 6. The difference between the figures begins with the sense coil,which is grounded at the top rather than the bottom and whose output,from the bottom via node 632, is applied to the non-inverting input ofunity buffer amplifier 550, whose output on 634 feeds back to theinverting input. The induced voltage output at 634 is therefore reversedin polarity compared to output 534 of FIG. 5. 634 connects to resistor602, which defines the input of an integrator consisting of amplifier604 grounded to ground 608 at inverting input node 606 and with parallelfeedback elements, capacitor 612 in parallel with field effecttransistor (FET) 614. The FET source and one side of 612 join to node610 leading to the inverting input of 604 along with input resistor 602.The FET drain and the other side of 612 join to node 616 at the outputof 604. The FET discharges capacitor 612 when line 652 from computer(CPU) 620 goes high, thus initializing the integrator to zero. Line 652is labeled “Off” since it initializes and shuts down the servo circuitwhen in its high state. The integral output is called “Φ” since thesignal varies in proportion to flux Φ. This flux signal on 616 isapplied to two non-linear circuits, at the denominator terminal 622 ofan analog divider 628, and at the input terminal 618 of a square-lawcircuit. The numerator terminal to 628 is node 626, which is also theoutput of the current-detection instrumentation amplifier alreadydefined by 530 in FIG. 5 and relabeled as 530 in FIG. 6. The output ofdivision circuit 628 is labeled “−I/Φ” inside the divider box, and alsoby “−Xeff” on the output node, since the ratio of current/flux yieldswhat has been defined as “effective X” and what approximates a linearmeasure of magnetic gap for small gaps. 630 is the basis for the motionterms of PID control. The proportional term is defined from 630 viainput resistor 668 to the inverting input of amplifier 633 at node 672.A reference is provided via computer 620 via bus 621 to digital/analogconverter (DAC) 650, yielding the reference “Xo,eff” on the DAC outputat node 654, which leads to input resistor 666 summing in with resistor668 into inverting input node 672. The proportional output from 633 atnode 676 leads to feedback resistor 670 back to the inverting input. 676also leads to summing resistor 674 to node 660, defining theproportional current term labeled “Prp.” The non-inverting reference for633 is provided at node 678 by ground 679. Node 630 generates anintegral term via input resistor 644 to node 642 at the inverting inputof amplifier 632. The DAC reference on 654 couples into node 642 viaresistor 638, defining a variable “zero” for both proportional andintegral terms. Integrator feedback capacitor 646 from output node 648to input node 642 is paralleled by initialization FET 656, with drain to648, source to 642, and gate to 652, so that 632 initializes at the sametime as 604. From node 648, resistor 664 turns the current designated“Int” into summing node 660. The non-inverting reference for 632 isprovided at node 658 by ground 662. Inverting input node 684 ofamplifier 636 generates a band-limited derivative term via output node630 and series components 680, a differentiating capacitor, and 682, aband-limiting resistor, leading to 684. Feedback from the output of 636is provided by gain-setting resistor 688 and band-limiting capacitor686, wired in parallel from the output back to node 684. Resistor 691completes the definition of the derivative current term, labeled “Dif”above 691, and summing into input node 660. The non-inverting referencefor 636 is provided at node 683 by ground 685. The proportional,integral, and derivative terms just described sum currents via 660 intothe inverting input of amplifier 690, whose output node 697 connectsback to the inverting input node 660 via gain-setting resistor 696. Thenon-inverting node 693 of 690 receives a bias term via resistor 694 frompotential source 698, “BIAS,” and from the output node 624 of square-lawcircuit 640 via resistor 695. The output of 640 on 624 is labeled “Φ²”and is the square of magnetic flux, which varies approximately inproportion to magnetic force. Hence, magnetic force is differencedagainst the sum of the proportional, integral, and derivative terms inamplifier 690. The resulting signal voltage differential, greatlyamplified, is applied via node 697 to the bottom side of drive coil 506,as shown in FIG. 5. The resulting current in 506 is measured via amp 530to give the signal at output node 626, completing the feedback loop.Thus, the high gain of the feedback loop through 690 insures thatmagnetic force tracks, with little phase lag, the sum of theproportional, integral, and derivative motion terms. To force the outputof 690 high and thus force the current in coil 506 to decay to zero,silicon diode 692 connects from “Off” line 652 on the anode side tonon-inverting input node 693 on the cathode side. When 652 goes high,this forward biases 692 and forces the output of 690 positive.

To identify the “outer” and “inner” feedback loops described moreabstractly earlier in this Specification, 690 provides a largeamplification to the difference between a force signal, varying roughlyin proportion to “Φ²” via wire 624, and a target force, consisting of abias force from 698 plus a transfer function of position via summingresistors 664, 674, and 691 for integral, proportional, and derivativecomponents of the transfer function. The “inner” loop causes net force,including magnetic and spring components, to track the target force withminimal time lag, due to the high gain of 690. The “outer” loop, not soapparent in the circuit schematic, involves the mechanical response ofthe armature of solenoid 500 to the controlled force. The mechanicalload is modeled conceptually as a mass, spring 504, and damper 505(recalling the labeling of FIG. 5). The mechanical transient andsettling behavior is modified by an equivalent electronic spring in thefeedback loop attributed to proportional gain via 674, by an equivalentdamper via 691, and by an equivalent active mechanical component, havingno passive mechanical counterpart, in the integral correction term via664, The net equivalent load, including mechanical and electronicfeedback components giving rise to equivalent net inertia, netrestoration, net damping, and cumulative or integral correctionbehavior, is the responsiveness of the outer loop. If the generation ofa change in force in response to an error signal at 690 involved asignificant time lag, then this lag, viewed as a transfer function,would be multiplied by the transfer function responsiveness of the netequivalent load, in many cases leading to an unstable system. By makingthe inner loop sufficiently fast and by providing adequate damping inthe outer loop transfer function, a servomechanism can be constructedthat is free of ringing and overshoot response to small signalperturbations. It is recognized that in responding to largeperturbations or large initial errors, the inner force-correcting loopof FIG. 6 will slew whenever the voltage drive signal from 690 is driveninto limiting and a significant time is required to bring magnetic fluxto match a target level. Recovery from slewing will include overshoot ifthe system is driven too hard and if electronic velocity damping doesnot provide enough “anticipation” to bring the system out of slewingbefore it is “too late.” By limiting the speed, particularly theacceleration, with which the parameter “Xo,eff” on the output of DAC 650is allowed to change, the designer can prevent unwanted overshoot due toslewing recovery.

An Oscillatory Solenoid Servo Circuit

With too much inner loop gain, the circuit of FIG. 6 could be prone tohigh frequency oscillation. The objective of the modifications turningFIG. 6 into FIG. 7 is to bring about such an oscillation intentionally,to assure that voltage-limiting associated with the oscillation causesno damage or waste of energy and is confined to the drive signal to coil506, and to assure that recovery from voltage limiting is very quick, inorder to prevent the oscillation from slowing down the corrective actionof the inner feedback loop. The continuous analog output of amplifier690 is an inefficient means of driving coil 506, a switching regulatorbeing preferred for efficient transfer of energy from a fixed DC supplyto an inductive load. Rather than stabilizing the analog feedback loopand providing a Class D switching amplifier within that loop as areplacement for 690, a more direct solution is to design a feedback loopthat is an oscillator providing a clean, variable-duty-cycle switchingsignal to the solenoid drive winding. In FIG. 7, amplifier 690 isreplaced by comparator 790. A small amount of regenerative feedback isprovided around the comparator from output node 715 via resistor 796 tothe non-inverting input, so that saturated switching is assured. Thecomparator output at 715 feeds into one input of two-input NOR gate 720.The “Off” signal from 652 feeds not via a diode as in FIG. 6, butinstead via node 752 to the second input of NOR gate 720, accomplishingthe same shut-down function. The output of 720 via node 725 drives thegate of N-channel enhancement-mode FET 730, whose signal inversionundoes the inversion of the NOR gate to restore the polarity of the FIG.6 feedback circuit to the circuit of FIG. 7. The source of 730 isgrounded while the drain at 797 connects to the bottom coil 506, as didthe output of amplifier 690. To permit recirculation ofinductively-maintained current, shottky diode 710 provides the samefunction performed by diode 510 of FIG. 5. In this oscillator, the errorsignal in the feedback crosses zero (neglecting the small hysteresisfeedback) each time the comparator output switches. With minimal phasedelay, the comparator circuit controls flux-squared, an indicator ofmagnetic force, rather than voltage or current. A voltage-drive feedbackloop, by contrast, would suffer from nonlinearity and in extremelyvariable phase lag due to gap-dependent inductance. The phase lagbetween voltage and flux is nearly independent of magnetic gap, and thehigh gain of the oscillator loop substantially reduces the effect ofthis phase lag on servo stability. Thus, the inner loop throughcomparator 790 functions much like the inner loop through amplifier 690,while the components of the outer servo loop remain unchanged from FIG.6 to FIG. 7.

Linear Approximations Simplify Oscillator Servo

FIG. 8 illustrates a modification of the circuit of FIG. 7 to eliminatethe operations of analog division and squaring. The approximationsinvolved were described under the heading “APPROXIMATE SERVO CONTROLMETHODS” particularly with reference to Eqs. 57 and 58, repeated here:A/B≅A 0/B 0+(A−A 0)/B 0−(B−B 0)(A 0/B 0^2) for A and B near constants A0 and B 0.  57]A ² ≅A 0 ²+2(A−A 0)A 0 for A near constant A 0.  58]

Instead of using a division circuit to compute the current/flux ratio,I/Φ, we utilize the approximation of Eq. 57 to approximate this ratio asa constant plus two linear terms, a positive term for variation of Iabout a reference I0, and a negative term for variation of Φ about areference Φ0. As in FIG. 7, a differential amplifier in FIG. 8 generatesa current signal on node 826 and labeled “I” while an analog integrator,initialized to zero output before the circuit is activated, generates amagnetic flux signal on node 816 and labeled “Φ.” For a circuit intendedto provide “soft landing” i.e. near-closure of the magnetic gap withlittle or no overshoot and therefore without bumping at full mechanicalclosure, the ratio approximation needed should work best as the magneticgap approaches zero. In this situation, force is typically approaching aconstant value, namely the force of the solenoid return spring plus anysteady load force that might be encountered. Fractional variations inforce are going to be small on approach to closure. Since (as notedearlier) force is more or less proportional to the square of magneticflux, more or less independent of gap for small gaps, a stable servocircuit will be producing a relatively steady magnetic flux on approachto full gap closure. Thus, the signal on 816 may be expected to approacha constant value. The Current signal on 826, by contrast, will exhibitsignificant fractional variation, with I varying more or less in linearproportion to gap X for small X. For a derivative signal to serve as thedamping term of the PID controller, therefore, the current signal I on826 is applied to the band-limited differentiation circuit surroundingamplifier 836, which is like amplifier 636 and the associated componentsfrom FIG. 6 except for the difference that signal input −I/Φ from FIG. 6becomes signal I in FIG. 8. The current signal labeled −Dif at resistor891 going from the differentiation output to summing node 860 istherefore analogous to the negative of the current on 691 and labeledDif in FIG. 6, and similarly in FIG. 7. Denominator variation is simplyignored in the derivative signal, and likewise for the integral signal.Integrator amplifier 832 receives the I signal from 826 via inputresistor 838 to the inverting summing junction, while feedback capacitor846 and field effect transistor (FET) 856 provide for signal integrationand resetting to zero. Note, however, that FET 856 is turned theopposite direction of 656, with its drain facing the amplifier invertinginput and its source facing the amplifier output, since in this topologythe amplifier output swings negative to give current signal −Int acrossresistor 864 between the integrator output and summing node 860. Whilethe “Off” signal 652 from the CPU is the same in FIGS. 6, 7, 8, and 9,non-inverting level shifting buffer 851 is provided between 652 and thegate of 856 to provide a more negative gate swing for cutoff.

The integrator based on amplifier 832 includes a bias voltage, labeledto at 862, which is applied via conductor 858 to the non-inverting inputof 832. In the circuit of FIG. 8, the final target for steady magneticlevitation is not a position, but a current, where current I equals Io.The circuit seeks out the position X for which the specified current loprovides just enough magnetic force to balance the steady mechanicalforces at that position. Targeting a current rather than a positionrepresents an important simplification in design for many practicalcircuits. If, for example, a minimum holding current is the practicalgoal of a servo circuit, then the design engineer will determine, fromprototypes, the largest minimum holding current that is guaranteed tomaintain gap closure under all operating conditions, with an appropriatesafety margin. For a circuit with good magnetic closure, this worst-caseholding current is generally a small fraction of the current levelneeded to close the open gap, and the power associated with that currentis lower than peak power roughly in proportion to the square of thecurrent reduction, where a switching regulator provides an effectiveenergy conversion rather than a simple resistive dissipation of supplyvoltage. A value for Io slightly above the worst-case or maximum holdingcurrent will result in servo closure toward a hovering gap at a smallvalue X, whose particular value is often of minor importance. As will beshown in FIG. 15, the addition of a small permanent magnet component inthe magnetic flux loop of the solenoid makes it possible to set theparameter Io=0. The permanent magnet then provides the entire holdingcurrent, and the servo circuit seeks out that position for which zeroaverage current is drawn. This levitation position will vary accordingto load, which is unimportant for many magnetic bearing applications.The important issue of often to rely entirely on a permanent magnet forlifting power while maintaining control with low-power correction signalfluctuating about zero.

For proportional feedback, the proportional “Prp” signal on resistor 674of FIGS. 6 and 7, which used the current/flux ratio signal, becomes twoseparate proportional terms in FIG. 8: a term “−Prp1” from the fluxsignal on 816 via resistor 874 to summing node 860, and a term “−Prp2”from the current signal on 826 via resistor 875 in series with resistor876 to ground. The node between the voltage divider resistors 875 and876 is applied to the inverting input of comparator 890, while summingnode 860 is applied to the non-inverting input of 890. A small amount ofregenerative feedback is provided around 890 to the non-inverting input,as was done via resistor 796 around comparator 790 in FIG. 7. Noticethat the equivalent inputs of 790 and 890 are reversed, so that thepolarities of the negative signals “−Int” and “−Dif” and “−Prp1” and“−Prp2” are reversed go give the equivalent polarity on the output of890 on node 815 as was derived on the output of 790 at 715. Theremainder of the FIG. 8 circuit is like that of FIG. 7, including a NORgate like 720 driving a FET like 730 to power the solenoid drivewinding.

The approximations made in going from the servo of FIG. 7 to that ofFIG. 8 include an error in the derivative feedback signal via 891, pluserrors in other terms whenever the circuit is far from its designoperating point and the linear approximations to the ratio and squarelaw governing equations become poor approximations. One effect of theresulting errors can be to cause a mixing of the desirably separatedynamics of the inner and outer feedback loops previously described,creating stability problems. In both simulations and empirical trials,circuits like that of FIGS. 8, 9, and 10 are observed to exhibitinstability below the frequency band of intentional oscillation,especially when the differentiating or damping gain, e.g. via 830, ispushed too high. If flux “Φ” is being pushed around aggressively by anouter feedback loop demanding large changes in force, then theapproximation of constant flux is invalidated, and current “I”multiplied by a constant scaling coefficient is no longer a goodapproximation of the ratio of current/flux, I/Φ” The circuits of FIGS.8, 9, and 10 are nevertheless effective in less demanding applications,and have economic advantages.

FIG. 9 illustrates the collapse of the two integrators of the circuit ofFIG. 8 into a single analog integrator. Magnetic flux no longer appearsin the circuit as a separate signal, but instead in combination with the“−Int” current signal across resistor 864 of FIG. 8. The new combinedintegral signal is free from long-term drift, since feedback through theelectromechanical servo loop automatically cancels drift. Integratorresistor 602, inherited from FIG. 6 in equivalent form in FIGS. 7 and 8,becomes resistor 902 in FIG. 9, summing into the inverting input ofintegration amplifier 932 along with the current signal across resistor938, which is equivalent to resistor 838 from FIG. 8. Amplifier 932looks like amplifier 832 of the previous circuit, except for theadditional flux derivative input on 902, but it also looks likeamplifier 604, inherited from FIG. 6 by FIGS. 7 and 8, except for thecurrent input on 938. One zero-reset with a single FET replaces the twinzero reset functions of the two FETs of FIG. 8. The integrator outputcurrent of resistor 964 into junction 960 is labeled with both −Prp1 and−Int, indicating that the sum of the proportional and integralcontributions is provided by the integrator output across the singleresistor 964, functionally replacing resistors 864 and 874. The signalon 960 is treated like that on 860, and the remainder of the circuit ofFIG. 9 is like that of FIG. 8. Lacking an explicit magnetic flux signal,the circuit of FIG. 9 is now inherently dependent on a signal other thanthe “position” signal I/Φ as a target for the integrating feedback loop,While the target signal is a current it] FIG. 9, the target signal ofFIG. 10 is a pulse duty cycle. This choice of control variables leads todifferent dynamic settling behavior of the servomechanism. Under therestricted circumstances of constant supply voltage and constant drivewinding resistance, a constant pulse duty cycle yields an equivalenttarget current in the long run.

Servo Controller With Auxiliary Position Measurement

For reasons of economy and mechanical simplicity and reliability,earlier circuits have derived all position information from electricalresponses of the solenoid winding or windings. Where the solenoid designpermits incorporation of a separate position sensor, performancecomparable to the relatively complicated “exact.” servo of FIG. 7 can beachieved without the use of a ratio circuit. The circuit of FIG. 9 ashares with FIG. 9 all inner feedback loop to control the linear fluxterm Φ, rather than the square-law term Φ². This linearizingapproximation results in a variable dynamic gain factor around the outerPID loop, because of the square-law response of actual force to changein flux. The system will therefore be underdamped or overdamped,sluggish or quick, depending on the operating region, but runawayinstability is not generally threatened by the linearization of the fluxcontrol loop. Of more consequence to stable performance is abandonmentof the current/flux ratio in favor of current as an approximate positionsignal. By use of an auxiliary position sense signal, loop stability isobtained even when high outer-loop gain is used to speed the settling ofan otherwise sluggish mechanical system, e.g., one characterized by alow spring rate and thus a slow natural period of oscillation. One has atradeoff, then, between a division operation in the control electronics(in analog circuitry as illustrated in FIG. 7, or in a real time digitalcontroller), or a separate sensor. (Another option, using oscillatorychange in current slope as a measure of position, is discussed laterwith reference to FIG. 12.) FIG. 9A illustrates the auxiliary sensorroute.

In FIG. 9A, the mechanical network in the middle of solenoid 500 hasbeen modified by the addition of a permanent magnet 970, whose polingdirection is indicated by an arrow, and the addition of a Hall effectsensor 974, indicated schematically as a balanced bridge whose output isamplified by amplifier 982. The Hall effect bridge and amplifier aresupplied by positive supply voltage via wire 978 and by negative supplyvoltage via wire 980. (in practice, since common Hall effect ICs oftenuse a low supply voltage, e.g., 5 volts, a separate single-sided supplymight drive the Hall sensor, while further circuitry might offset themid-scale sensor output to zero volts.). Line 972 from the armature ofsolenoid 500 to magnet 970 indicates a mechanical connection, so thatthe magnet moves with the armature. Line 976 similarly indicates amechanical linkage from the stator of the solenoid to the Hall sensor,which is therefore fixed in space. The Hall sensor output connects via984, labeled “X” for the position signal, to the non-inverting input“+A” of feedback-controlled gain differential amplifier 986, with normalsignal gains +A and −A from the two inputs. Digital/Analog Converter orDAC 950, unlike its counterpart 650, provides the target parameter,“Xtgt,” to which “X” is compared. This target output of 950, via 952, isapplied to the inverting “−A” input of amp 986. The difference outputfrom 986 on wire 988, labeled “X-Xtgt,” performs much the same functionas the position-approximating signal “I” seen originally at 826 of FIG.8 and carried unchanged to FIG. 9. A difference is that the bias levelprovided via resistor 866 from the DAC in FIG. 8 is not summed directlywith the position sense signal for input to all the legs of the outerservo loop, namely the proportional, integral, and derivative paths.Hence, if Xtgt is varied, the damping feedback path will “feel” thevelocity of the target variable and generate a quick response to followtarget changes. The proportional gain of the loop with respect to themeasure or position is labeled “−Prp2” as in earlier figures, while thebalancing magnetic flux signal gain is labeled “−Prp1” as before. TheSignal used as a measure of position has changed, but the basicfunctioning of the servo loop is the same except for the elimination ofsome performance-limiting errors.

An example of the mechanical configuration of a Hall effect sensor andpermanent magnet is shown as part of FIG. 14, along with numerouscomponents to be discussed later. The sensor actually uses a pair ofmagnets, whose poling is oppositely oriented, moving on a holder oneither side of the Hall effect device. Solenoid 1410 is based on two potcore halves drawn together by the magnetic field bridging across theinner and outer gaps. 1410 is configured as a “pull” solenoid (or withspring bias toward pushing, as a “push less” solenoid) with the pullingend pointed down and the sensor occupying the unused “push” end. Plasticmagnet holder 1480 is secured to the end of the solenoid shaft by screw1402. Flat circular magnets 1482 and 1484, seen in section, are poledrespectively downward and upward, as indicated by arrows diagrammed inthe magnet sections. The Hall integrated circuit 1486 extends out of thebottom of PC board 1488, which in turn is mounted on the surface ofhousing closure component 1490. The direction of vector sensitivity ofthe Hall device points from left to right in the diagram, the front sideto the back side of the package. The magnetically sensitive region isoff-center in the package and actually lies nominally midway between themagnets, even though the package itself is off-center. The field of thetwo magnets describes a clockwise loop out of the top of 1484, laterallyright to the top of 1482, down and out the bottom of 1482, laterallyleft to the bottom of 1484, and completing the magnetic flux path tipthrough 1484 and out the top. When the magnets move up, it places theHall sensor lower relative to the magnets, in a region of flux fromright to left, which opposes the vector sensitivity of the device andcauses a negative-going output. A downward armature and magnet movementsimilarly places the Hall sensor higher relative to the magnets, in aleft-right field producing a positive-going output. The downwardmovement of the armature pot core half, which is below the stator potcore half, opens up the magnetic gap and therefore increases thevariable “X,” so positive Hall sensor variation corresponds to anincrease in X.

Servo Controller With Precision Measurement Capability

The circuit of FIG. 10 is similar in function to that of FIG. 9, butdiffers in four significant respects. First, the circuit detects drivecoil current without the use of a sense resistor in the drive coilcircuit, relying instead on inference of the drive coil current from thecurrent-times-resistance voltage drop in the drive winding, astransformed into a sense winding voltage when the drive voltage isturned off. Second, the integral feedback of the circuit is a measure ofpulse duty cycle, rather than of coil current. Third, the circuitsupports slow release from a nearly-closed state under servo control.Fourth, the circuit supports precision measurement of shuttle positionbased on the ringing frequency of the drive winding inductance resonatedagainst a capacitor. This position measurement via resonance is referredto as “pinging.” The resonating capacitor 1063 can be disconnected fromthe solenoid circuit by use of optical switch 1087. A high impedancecurrent source circuit built around amplifier 1090 and FET 1099 is usedboth to excite ringing and to provide a selectable DC current biasthrough the drive winding during the ping measurement of position. TheDC bias generates an electromagnetic force bias. The objective is tomeasure the mechanical compliance of the solenoid load, i.e., thevariation in position, as determined by pinging, with respect tovariation in force, as determined by computation from the DC currentbias and the pinging frequency.

Examining the circuit in more detail, the solenoid at 1000 is likesolenoid 500. The top of the drive winding is connected to positivebattery terminal 1029, labeled Vb,” which is also a node common to theanode of zener diode 1091, the cathode of shottky barrier diode 1096,and one side of “ping” capacitor 1063. The bottom of the drive winding,opposite the positive battery terminal, is driven via node 1086 by thedrain of FET 1085, whose source is returned to common ground, which isalso the negative battery terminal. Associated with the drive windingare several components for sustaining a recirculating current, impedingand slowing the recirculating current, and pinging. Shottky diode 1096,for conducting an inductively-sustained recirculating current when poweris not being applied via FET 1085, has its anode connected to node 1086via a bi-directional FET which is part of optical switch 1088, the gateof the FET being activated effectively by light from a photodiodecomponent of 1088. The anode of this photodiode is connected toregulated supply 1028, called “V+,” via node 1030, while the cathode ofthe same photodiode is returned via current-limiting resistor 1093 towire 1094, labeled “Pclamp” for the logic level associated with theclamp operation as part of the Ping circuit. This logic level isprovided by a microprocessor pin, possibly via a buffer, with a lowlogic level turning on the optical switch and connecting diode 1096 torecirculate drive winding current with a minimum of voltage drop. Thenthe “Pclamp” logic level on 1094 goes high, cutting off photodiodecurrent, then optical switch 1087 opens, preventing current flow through1096. Inductively sustained current is then forced in the forwarddirection from node 1086 and the anode of diode 1097 through to thecathode of 1097, and from there to the cathode of zener diode 1091 andin the zener-drop direction of 1091 to the anode of 1091, which isconnected to positive battery terminal 1029. Thus, causing Pclamp to gohigh forces recirculating drive cut-rent to pass through the brakingpath of zener 1096, reducing the current level quickly. Capacitor 1063is connected in parallel with the drive winding except for opticalswitch 1087, whose turning off effectively eliminates the capacitor fromthe circuit. Specifically, one terminal of 1063 connects to batterypositive terminal node 1029, the opposite terminal or 1063 connects to alead of the bi-directional optical FET in optical switch 1087, and theother optical FET lead connects to node 1086. The photodiode in switch1087 has its anode connected to the regulated positive supply at node1030, with the cathode connected via current limiting resistor 1067 towire 1065, which is energized by the logic level labeled “Pcap” for Pingcapacitor. When Pcap goes high, no photodiode current flows andcapacitor 1063 has no significant effect on the drive winding, while alow logic level at Pcap and 1065 drives photodiode conduction, turningon the FET and connecting capacitor 1063 in parallel with the drivewinding.

Pings, or resonant ringing signals, in the resonant circuit consistingof the drive winding and capacitor 1063, become energized in severalways. If current has been driven via drive FET 1085 and decays slowlyvia 1096, and if switch 1087 is switched on during this conductionperiod, then a low-level ping will occur as decaying conduction through1096 comes to a stop, with a first peak at less than the shottky forwardbias of 1096. If 1096 is isolated by an off state in switch 1088,causing current to decay rapidly through the zener circuit via 1091,then the cessation or zener current will be accompanied by a much higherlevel ping, with the first AC peak somewhat below the sum or the zenerdrop plus the forward drop of diode 1097. For a controlled pingamplitude, current may be stopped by the braking of zener 1091 beforethe capacitor path is connected through on-state switch 1087, afterwhich current pulses may be applied via the high impedance currentsource circuit source circuit consisting of FET 1099 and amplifier 1090.The drain of 1099 is connected to node 1086 while the source of 1099 isconnected via current-scaling resistor 1021 to the common ground atlabel 1025. The node common to the FET source and resistor 1021 isconnected to the inverting input of 1090, resulting in a feedbackvoltage precisely proportional to the drain current of 1099. Thenon-inverting input of 1090 at node 1001 is biased via resistor 1017 toground at 1025 and via resistor 1009 to the negative supply labeled “V−”indicated on wire 1013. This negative supply may be provided, e.g., by aswitching inverter operating from the positive battery voltage “Vb” from1029. The bias level to the non-inverting input of 1090 is varied by twologic levels: “Ping1” on wire 1098 and via resistor 1005 to node 1001;and “Ping2” on wire 1008 and via resistor 1015 to node 1001. Like “Pcap”and “Pclamp,” the signals “Ping1” and “Ping2” are logic levels eitherdirectly on microprocessor pins or obtained via buffers, swingingbetween ground potential and a positive logic supply voltage, e.g., “V+”at 1028. When Ping1 and Ping2 are both low, the current source is offbecause of the negative bias via 1009 from 1013. For combinations withone or both of Ping1 and Ping2 being high, resistor ratios are chosen togive desired choices of bias voltages and current source output levels.Switching between current levels (including zero) either as steps or aspulses can be used for dual purposes: to excite ringing for frequencydetermination, and to maintain a chosen magnetic force in the solenoidarmature. By varying force bias and measuring changes in ping frequency,the circuitry is used to measure mechanical impedance of devices drivenby the solenoid, including to determine compliance due to the presenceof bubbles in a solenoid-driven pump.

Unlike solenoid servo circuits of earlier figures, the circuit of FIG.10 lacks a current sense resistor. The level of current in the drivewinding is inferred, instead, from the voltage induced in sense winding1007 when current is recirculating through on-state switch 1088 anddiode 1096. The total voltage drop balanced against induced voltage inthe drive winding is given by I·R+Vd for current I multiplied by netresistance R (including mostly the winding, plus an increment for theon-state switch) and for diode forward drop Vd, typically a smallvoltage for a shottky device. Coil 1007 is grounded at its upperterminal at 1034 and connected from its lower terminal via 1022 to thenon-inverting input of unity buffer amplifier 1020, whose output vianode 1024 couples back to the inverting input of 1020. The signal on1024 goes negative when FET 1085 switches on to drive an increasingcurrent, and positive when current is recirculating and being slowed bya combination of resistive voltage drop and diode voltages. 1024connects to terminal 1040, labeled “ADC” and indicating ananalog/digital interface to a control microprocessor. 1040 may be amulti-bi-analog/digital converter, or it may be a comparator (i.e. aone-bit A-to-D) serving as input to a period counter. Circuitryincluding both a multi-bit converter and a comparator may be included inthe “ADC’ device at 1040, depending on the measurement functions chosen.For determination of solenoid armature position, it is possible toanalyze samples from a multi-bit ADC waveform to determine a best-fitfrequency of a ping signal, or alternatively it is possible to rely ongreater time resolution of transitions from a comparator output toobtain a ringing period or frequency. If frequency is varyingdynamically with time due to motion or the solenoid armature, thecomparator option offers perhaps the simpler form of signalinterpretation. An application to be discussed in relation to FIG. 14 isdynamic bounce of the armature as the solenoid is de-energized and thean-nature is pushed by return spring force into a diaphragm backed bywater and, possibly, bubbles. The multibit ADC is useful for monitoringand analyzing overall circuit performance, specifically in the tellingindications of induced voltage trace 1] 80 of FIG. 11, whose polarity isthe opposite of the signal connected to ADC terminal 1040.

As mentioned, the buffered induced voltage signal on 1024 is positivewhen drive transistor 1085 is off and current is decaying in the drivewinding. In the case where optical itch 1088 is on and the “slow decay”mode is active, the signal on 1624 varies with the sw resistive voltageI*R, and this current-indicating signal passes via the anode of shottkydiode 1033 to the cathode of that diode, then via small resistor 1036 tonode 1058 and to the source of FET 1056. When 1056 is on, the signal via1033 and 1036 conducts to the drain of 1056 and on to node 1069 andsample/hold capacitor 1062, whose opposite terminal is grounded. FET1056 is switched on when FET 1085 is off, so that 1062 is connected forband-limited sampling (with bandwidth limit set in part by resistor1036) of the current signal, I·R, from buffer 1020. When the drive coilis actively driven and induced voltage is not an indication of currentalone, the signal on 1024 is negative, 1033 is reverse-based, FET 1056is off, and the drain of 1056 points toward the positive sampledvoltage, preventing leakage of the sampling capacitor charge back viaresistor 1054 to ground. From node 1058, resistor 1054 to ground at 1039provides a discharge path for capacitor 1062 when the current signallevel is decreasing from one sample period to the next, thus allowingthe output of the sample/hold circuit to decrease. Amplifier 1060 servesas a unity buffer for the sampled voltage, with its non-inverting inputconnected to capacitor 1062 at node 1068, and with ks output connectedvia no, c 1064 to its own inverting input and to two output paths. Onesuch path, representing proportional gain of the current signal, is viaresistor 1066 to the inverting input of comparator 1079, whose inputalso includes a programmable bias from a digital/analog converter or“DAC’ consisting of the group of four resistors 1050 driven by the fourbits of the DAC input signal, on bit lines collectively labeled 1048 andindividually labeled MAU,” MAC I,” “DAC2,” and “DAC3.” The other signalpath for the current sample/hold signal is via phase lead capacitor 1070and band-limit resistor 1071, wired in series to the inverting input ofdifferentiation amplifier 1076, The non-inverting input of 1076 isgrounded, while the feedback from the output on node 1075 consists ofparallel gain-setting resistor 1074 and band-limiting capacitor 1072,both wired to inverting input node 1073 and the input from 1070 series1071. The differentiator output on 1075 sums via resistor 1077 to thenon-inverting input of comparator 1079, along with another input signalvia resistor 1046 and a regenerative or hysteresis feedback signal vialarge resistor 1080 From the output of 1079 on node 1081.

Leaving the “current” or I.R” signal path momentarily and returning tothe overall induced signal path, the output of 1020 on node 1024 sumsvia resistor 1026 into the inverting input node 1037 of invertingintegrator amplifier 1032. Integrating feedback is achieved by feedbackcapacitor 1038 from output node 1044 of 1032 back to input node 1037.This capacitor can be shorted by FET 1042, whose drain connects to opamp output node 1044 and whose source connects to input node 1037, thusbeing wired for a normally-positive integrator output. Shorting viaon-state FET 1042 resets and holds the integrator output to nearly zerovolts whenever the signal “OFF” at 1041, and communicating via node 1043to the FET gate, is high. Two other signals sum to the integrator inputat 1037: a negative bias from negative supply 1003, “V−,” via resistor1002 to 1037, and a logic level via resistor 1016 to 1037 from node1014, which is the output of NOR gate 1012.

We now consider circuit operation for combinations of logical levels1041 and 1011, “OFF” and “OPEN.” First consider the “normal” situationwhere “OPEN” on 1011 is low, i.e., no call to open the solenoid. When“OFF” on 1041 and via 1043 is high, integrator 1032 is initialized tozero. At the same time, the high “OFF” signal is applied via 1043 to oneof the two inputs to NOR gate 1082, forcing that NOR output low on 1083.1083 connects to the gate of drive transistor 1085, forcing it off. 1083also connects to both inputs of NOR gate 1084, which acts as a logicinverter. The output of 1084 drives, via node 1052, the gate ofsample/hold FET 1056, thus causing that FET to be on, sampling, when FET1085 is off, and vice versa, off, holding, when 1085 is on and drivingthe drive winding. 1052 also connects to one of the inputs of NOR gate1012. With “OPEN” on 1011 and 1010 in its “normal” low state, NOR gate1012 behaves like an inverter to the signal on 1052, so that the signalon node 1014 at the output of 1012 reflects the state of driver FET1085, namely, high when 1085 is on and low when 1085 is off. When “OFF”on 1041 and via 1043 is high, as discussed, driver FET 1085 is kept off,and the integrator is initialized. When “OFF” goes low, the soft-landingfeedback loop is activated. Drive FET 1085 is enabled to follow theinverse of comparator output from 1079 via 1081, turning off when thecomparator output is high and on when the comparator output is low. Inthis case, the signal summation into integrator 1032 is analogous to thesummation into integrator 932 of FIG. 9, the sum of an induced voltagesignal plus a drive signal, except that in this case the drive signal isa logic level indicating the on or off state of the driver FET, ratherthan being a current signal. The integrator thus responds to the runningaverage, or duty cycle, of the drive signal. The “target” of theintegrator feedback loop is to establish a steady on-state duty cyclewhere the induced signal from the sense coil averages zero and the ratioof resistors 1016 and 1002, and voltages 1003 (negative) and on-statevoltage of 1014 (positive) establish a zero average balance, causingzero long-term cumulative change at the integrator output. Thus, if theresistances of 1016 to 1002 are in a ratio of 1:3 and if the on-statevoltage From 1014 equals the magnitude of the negative bias on 1003,then a duty Cycle of 1/3 at 1014 will result in an average of zerocurrent to the integrator, implying an equilibrium. While this is theultimate target for soft landing, i.e. a duty cycle corresponding to anequilibrium armature position typically near magnetic Closure, theshort-term dynamics of remaining stably near the equilibrium positionare established by sampling of current and proportional and derivativefeedback of current, plus proportional feedback via integration of thesense winding output, i.e. proportional feedback of the flux or Φsignal.

Circuit operation is simplest when the sampled current feedback path viaFET 1056 is deactivated, e.g., by removing diode 1033, and whenintegrating duty cycle feedback is deactivated, e.g., by removingresistors 1002 and 1016. In this situation, the integral output on 1044represents total magnetic flux, and is compared to the DAC voltage onthe inverting input of comparator 1079. An increase in flux is indicatedby an increase in the integrator output on 1044, which via resistor 1046communicates to the non-inverting input of comparator 1079 and tends todrive the comparator output high. The inversion of the comparator signalat NOR gate 1082 results in FET 1085 being turned off, initiating a rateof decrease in magnetic flux. Thus, the simplest circuit operationmaintains constant flux, resulting in a magnetic force field thatincreases somewhat with decreasing magnetic gap X. The force increase ismoderate even as X tends to zero. The transient response of the servosystem under these conditions is a damped sinusoid in X, except that avery low-rate mechanical spring may fail to overcome the slightlydestabilizing effect of magnetic force variation with gap, so thatdivergence to full-open or full-close is possible. The other feedbackloops, dependent on sampled coil current and on the integral of dutycycle, may be used to provide an approximation of velocity damping,provide a stabilizing spring-like magnetic force, and provide long-termre-biasing of flux to drive X to a value in equilibrium with a targetduty cycle. As with the circuits of FIGS. 8 and 9, excessive feedbackgains involving sampled current and/or duty cycle result in loss ofstability.

The “PID” signals (of Proportional, Integral, and Derivative feedbacks)added to the dynamics of the basic flux servo circuit (described above)include the duty cycle integral (a sort of integral feedback of positionerror), plus the value of sample current (generating a stabilizingmagnetic spring rate) and the time-derivative of sampled current,providing limited levels of approximate velocity damping. Theproportional feedback of the current signal via resistor 1066 may be setto zero by setting the resistance of 1066 to infinity (i.e. open). Ifthe mechanical spring rate encountered by the solenoid armature is low,then the relatively small change of magnetic force with respect tosolenoid position at constant flux may be sufficiently large, anddestabilizing, to overcome the stabilization of the mechanical spring.In that case, stability can be achieved by proportional feedback of thedrive current signal via resistor 1066. The polarity of this feedbackwould appear to be regenerative, since an increase in the current signalfrom 1064 via 1066 drives the comparator output low, which via theinversion of NAND gate 1082 drives FET 1085 on, which tends to furtherincrease current. Consider, however, the tendency of current, in theshort term, to be driven by magnetic gap width X, so that reducing Xdrives current down and increasing X drive's current up. Further, with aweak or approximately constant-force spring, a more or less constantmagnetic force demands a lower current at a lower gap X and a highercurrent at a higher gap X. One can say that the proportional currentfeedback via 1066 rebiases this equilibrium relationship so that atlower current, indicating reduced gap X, current is driven still lowerthan it would have been without feedback via 1066, thus reducing themagnetic force of attraction and making X (end to increase. Conversely,a higher current, indicating increased X, causes current to be driveneven higher, increasing magnetic attraction and tending to close X Alittle bit of feedback across 1066 thus acts like a stabilizingmechanical spring, and both simulation and experiment with theclosed-loop circuit confirms that soft landing with a nearlyconstant-force mechanical spring is made possible, using the circuit ofFIG. 10, by the inclusion of a limited amount of proportional currentfeedback. Other forms of feedback around the loop, principally thedegenerative feedback adjusting current to stabilize magnetic flux, giverise to overall circuit stability. If too much proportional currentfeedback is generated, the regenerative aspect of this feedback loopmanifests itself as ringing responses and, at excessive “spring-rate”gain, instability. Similarly, if too much “velocity” feedback isgenerated via the band-limited current differentiation via resistor1077, then the damping effect is progressively lost with furtherincreases in “velocity” feedback until stability is lost. Theapproximations of a circuit like that of FIG. 10, and specifically theerrors in those approximations, set boundaries to the feedback levelsthat call be employed to good effect. Within stable boundaries, however,the circuit of FIG. 10 and similar earlier circuits are economical andeffective.

Consider finally events accompanying the setting of “OPEN” on 1011 and1010 to a high logic level. “OPEN” is normally kept low until softlanding and stable hovering are accomplished, with “OFF,” being heldlow. In certain applications it is desirable to re-open a nearly closedsolenoid smoothly, somewhat slowly, and under servo control. One reasonis to reduce the noise thump of opening. Another reason is to allow asolenoid-driven fluid control valve to close somewhat slowly to avoidfluid cavitation. When “OPEN” goes high with a nearly closed solenoid,the action of NOR gate 1012 is to inhibit the duty cycle feedback paththat established all equilibrium gap X, forcing the duty cycle signal on1014 to remain low. This leaves the bias current from resistor 1002unbalanced by a duty cycle. The servo circuit will behave as if themagnetic gap X had shrunk to zero and will respond with a progressiveincrease in the target signal for magnetic flux. More particularly, thenegative signal via resistor 1002 will be inverted on integration toproduce a positive-going ramp on 1044. As the feedback loop responds,the primary effect is to produce a negative-going ramp in magnetic flux,which via coil 1007 and follower output signal 1024 will generate apositive current through 1026 offsetting the negative current through1002. The “target” for magnetic flux is thus driven toward zero in alinear ramp, with some modification caused by the action of the sampledcurrent feedback path. The immediate effect of switching “OPEN” to ahigh state is to drive the comparator Output on 1081 high a largerfraction of the time, which will reduce the “on” duty cycle of FET 1085and thus initiate a re opening of the solenoid gap. Feedback derivedfrom sense coil 1007 will balance the open-loop tendency and result in asmooth and progressive reduction in solenoid magnetic force and acorresponding smooth opening. The re-opening rate can be decreased byconnecting a resistor between node 1010 and node 1037, thus causing thehigh logic level on 1010 to partially offset the negative bias currentvia resistor 1002. The re-opening rate can similarly be increased byinverting the signal on 1010 and applying that inverted signal via aresistor to node 1037. Without such modification, the rate re-openingunder servo control will correlate with the rate time constant set forintegral feedback response to pulse duty cycle.

FIG. 11 shows signal waveforms associated with the operation of thecircuit of FIG. 10. The chart at 1100 is a multi-trace graph against ahorizontal scale in milliseconds, extending, e.g., far 90 millisecondsfrom beginning to end, as indicated by labels. Progressing from bottomto top trace, trace 1110 and labeled “Vd” is the drive logic level seenat 1083 or FIG. 10. Trace 1120 is current “I” flowing through the drivecoil, but not directly measured in the circuit of FIG. 10. Trace 1130 is“Is,” or sampled I, appearing at node 1064 of FIG. 10. The derivativecurrent signal of trace 1140, labeled “dls/dt,” appears at 1075 of FIG.10, except with a polarity inversion in the circuit compared with trace1140. Note that trace 1140 is clipped for four positive spikes early inthe trace, and the spikes go higher than the graph shows. The truevelocity trace 1150 is labeled “dX/dt.” It is seen that trace 1140 bearslittle resemblance to true velocity until the magnetic gap is well onthe way to closure, after which time trace 1140 is a reasonableapproximation for velocity and thus an aid in damping of solenoidmotion. Trace 1150 shows gap X, which is seen to exhibit mild overshootand ringing. An decrease in circuit “velocity” damping results in agreater ringing amplitude, but an increase in damping feedback alsoincreases the ringing amplitude, with a high-frequency wobble showingup. Trace 1170 shows the induced voltage signal “Vi” whose inverseappears at node 1024 of FIG. 10. The time integral of 1170 is trace1180, “Phi,” which does not appear as a separate signal in the FIG. 10circuit.

Examining circuit operation, an initial bias from the DAC at theinverting comparator input drives Vd high. Until Vd spikes low, there isno sampled current feedback on traces 1130 and 1140. After a fewmilliseconds, the increase in flux Phi on trace 1180 causes Vd to spikelow, but this spike is reversed, and Vd is driven immediately highagain, by the feedback paths involving sampled current, traces 1130 and1140. During this “launch” phase, the flux target is drivenregeneratively upward and the drive pulse on 1110 continues with littleinterruption. The regenerative feedback eventually runs its course andthe system proceeds into a “trajectory” phase with Vd low and thecombination of magnetic and kinetic energies carrying the solenoidshuttle toward magnetic closure. The rebound from maximum closure bringsthe corrective feedback processes into play, resulting in a time varyingpulse duty cycle on Vd and a settling of the system. If the DAC bias isset higher, the solenoid bumps at full closure, while a lower DAC biascauses the solenoid to undershoot, well short of full closure, and pullclosed more gradually with a substantial increase in energy consumption.The traces shown represent roughly the minimum energy setting for theDAC bias. It is possible to adjust the circuit parameters for less pulseduty cycle integral feedback and more sampled current feedback,resulting in closure with little or no overshoot and no continuedringing. When the system is adjusted this way, it has a very narrowmargin of stability when load forces are varied, and small errors insetting the DAC bias, either too high or too low, result in instabilityand chatter of the solenoid. The adjustments illustrated in FIG. 11 arefor comparatively robust performance, but with the compromise of poorersettling than for the fast-settling parameters. A dynamic computersimulation of servo operation, as was used for the traces of FIGS. 1, 2,3, 4, and 11, is an almost indispensable design tool for making thiscircuit work, given the many nonlinear parameter interactions that mustbe explored. Actual circuit performance has correlated very well withsimulated performance. The equations from which the simulation wasdeveloped appear earlier in this writeup.

Log Domain Servo Oscillator

FIG. 12 illustrates how analog computation in the log domainsubstantially simplifies the hardware I'M a functional equivalent of thecircuit of FIG. 6 while incorporating the advantages of the oscillatoryapproach of FIGS. 6 and beyond. The FIG. 12 circuit maintains anabsolute position reference via AC inductance measurement. Thus, thecircuit takes control quickly from any starting position and initialconditions, exhibiting better settling and more robust behavior than waspossible with the approximations of the circuit of FIG. 10. Not countingthe ping and current source functions of that earlier circuit, thecircuit of FIG. 12 requires somewhat more electronic hardware. Thiscircuit relies entirely on current sensing and uses no sense coil.Solenoid 500 is like that of FIG. 5 in its mechanical configuration,except that there is no sense coil shown or used in the FIG. 12 circuit.The drive transistor is 1242, an enhancement node FET like those shownin earlier circuits, connecting to ground at the source and from thedrain to the bottom of drive winding 506, with the gate signal comingfrom node 1230, the drive logic signal called “Vd” and whose waveform isillustrated at 1240. Positive voltage supply 528, labeled “V+,” connectsvia current sense resistor 524 to the top of winding 506 and to resistor1245, at the inverting input of balanced differential amplifier 1250.The positive supply at 528 also connects to resistor 1247 at thenon-inverting input of 1250. Shottky barrier diode 510 provides acurrent-recirculation path from the bottom of 500 and the drain of 1242,on the anode side, up to positive supply 528 on the cathode side. Atdifferential amplifier 1250, matched resistors 1245 and 1247 formvoltage dividers with matched resistors 1246 and 1248, which connectrespectively between the inverting and non-inverting inputs of 1250 andground on the opposite side of the resistors. Since the common modevoltage coming into the differential amplifier approaches the positivesupply voltage and may exceed the input range of the operationalamplifier, this voltage division brings the common mode signal at theamplifier inputs to a lower level. Feedback resistor 1249 from theamplifier output on node 1251 to the inverting input is counterbalancedby matched resistor 1252 from the non-inverting input to ground, thuspreserving the balance for differential amplification. The currentwaveform on node 1251 is illustrated by trace 1254, labeled “I:” andshowing an exaggerated sawtooth waveform of current as it fluctuateswith voltage switching. The zero current level is indicated by a dottedbaseline below the trace. The amplitude of this kind of high-frequencysawtooth fluctuation in current is too small to show up in a trace like1120 of FIG. 11. Band-limited differentiation amplifier 1260 emphasizesthe switching-frequency AC component of current, using input capacitor1256 and band-limiting resistor 1255 to the inverting input of 1260, andparallel scaling resistor 1257 and band-limiting capacitor 1258 in thefeedback path from the output on node 1261. The non-inverting input of1260 is returned to ground. The band limiting of the amplifier may inmany instances be only a matter of maintaining stability while pushingfor the broadest practical differentiation bandwidth. An alternativeapproach to differentiation is to use, in addition to the current senseresistor, a small current-sense inductor or a current-sense transformerwith low mutual inductance between primary and secondary, so that thetransformer output voltage buffered at high impedance represents thetime derivative of current. Whatever the differentiation method, thedifferentiated waveform is, illustrated by trace 1270 and labeled “−/:”where the dot above the “I” designates time differentiation. The dottedline running through the solid trace is the zero line. The negativespikes of trace 1270 vary in amplitude very nearly in proportion toeffective magnetic gap X, since they vary in proportion to a fixedsupply voltage multiplied by reciprocal inductance, which is known to bea measure of X. The effect of coil current is to reduce the magnitude ofthe negative spikes slightly, and more or less in proportion to X, sothat the outcome as perturbed by resistive voltage loss remains nearlyproportional to X. This AC approximation of X, based on current slope,is a better measure of position than is winding current, as was used,e.g., in the FIG. 10 circuit. Amplifier 1280 and associated componentsfunction as an operational rectifier and inverter for the signal on node1261. Specifically, 1261 couples to input resistor 1271 to the invertinginput of 1280, whose non-inverting input is grounded. There are twofeedback paths from the output to the inverting input: via shottky diode1274 going anode to cathode from inverting input to output and clampingthe op amp output of a small negative peak; and via oppositely directedshottky diode 1275 From the output (on the anode side) to seriesresistor 1272 (oil the cathode side), which resistor in turn connects tothe inverting input. The signal at the junction of diode 1275 andresistor 1272 is the half-wave rectified and inverted, originallynegative spikes from 1261. Feedback action effectively cancels the diodedrop offset at the junction of 1275 and 1272, which node is connected tothe source of FET 1281. The gate of 1281 goes high, turning the FET on,when current is ramping up on waveform 1254 and when waveform 1270 isspiking negative. Conduction from source to drain charges sample/holdcapacitor 1283, whose opposite terminal is grounded, with resistor 1282between 1283 and the drain of 1281 providing enough band limiting andresistive impedance to maintain stability of amplifier 1280.Non-inverting buffer amplifier 1290 connects, at its non-invertinginput, to the junction of 1282 and 1283, with the output on node 1210feeding back to the inverting input. The sampled output on 1210 isillustrated by waveform 1200, labeled “I>0:” because it representscurrent slope sampled when that slope is positive and stored with thecurrent slope input is negative. This signal also approximates effectivemagnetic gap X The signal is used in two ways. First, proportional andderivative signals for position and velocity feedback are control led byresistor 1217 (proportional term) and capacitor 1216 (derivative term),with resistor 1215 in series with 1216 limiting the bandwidth ofdifferentiation. The series/parallel components just described connectbetween node 1210 and the inverting input of log amplifier 1204, whosenon-inverting input is grounded. An additional summing signal comes fromdigital/analog converter 1227, labeled “DAC2,” via input resistor 1214to the inverting op amp input. The DAC2 signal represents an effectiveintegral feedback correction, based not on a single shot of the solenoidbut on the performance over recent operations, interpreted by softwareto give the correction. The sum of the three input currents to theinverting input of 1204 is intended to be always positive, and this sumcurrent is drawn by the collector of NPN transistor 1208, whose base isgrounded and whose emitter connects to the op amp output, forming atraditional logarithmic amplifier topology with a negative log signal atthe output, which is labeled “−log(F)” since it varies as the “targetparameter” or target force of the servomechanism, the output of the“outer loop” feedback circuit and target of the “inner loop” feedbackcircuit described in the “OBJECTS OF THE INVENTION” and “SUMMARY OF THEINVENTION” sections. The positive current slope parameter on 1210 isreused at resistor 1213) to the inverting input of log amp 1203, Whichuses NPN transistor 1207 in analogous fashion to 1208 of the earlier logamp, generating a signal labeled “−log(I>0). The signal on 1210 alsoconnects to the input of analog/digital converter 1221, labeled “ADC,”whose output on bus 1222 provides input to the Computer 1223, labeled“CPU.” On the balancing side from log amps 1203 and 1204, amp 1202balances 1203, and amp 1201 balances 1204. The input to 1201 comes fromdigital/analog converter 1225, labeled “DAC I,” via input resistor 1211,while NPN transistor 1205 is matched to and thermally coupled to 1208for a balanced log comparison. The output from 1201 is labeled“−log(denom)” and represents the dynamically fixed but reprogrammabledenominator of the log balance equation. Log amp 1202 is driven by thecurrent signal from 1250 via node 1251 to input resistor 1212, while NPNtransistor 1206 is a match for transistor 1207 for the balanced logcomparison. The output of 1202 is labeled “−log(I)” in represents thecurrent term in the balance equation.

Magnetic force F_(m) varies roughly according to the equation:F_(m)/denom=(I/X)², where gap X is approximated by the signal “I>0,” anddenom is a denominator scaling constant. This magnetic force shouldmatch the target force F appearing in logarithmic scaling on the outputof 1204. Setting F_(m)=F and multiplying through the X-squareddenominator yields the expression:F·X ²=denom·I ²

Taking the log of both sides of this equation and substituting I>0 for Xyields:log(F)+2·log(I>0)=log(denom)+2·log(I)

The factors of 1 and 2 for linear and square terms are provided by theratios of resistors 1232 and 1233 from amps 1202 and 1203, labeled “R”for resistance R, and resistors 1231 and 1234 from amps 1201 and 1204,labeled “2R” for double the resistance at 2R, giving therefore half theweighting of the terms associated with the one-times resistance R. Thesides of 1231 and 1232 away from the log amps join at node 1218,connecting to the inverting input of comparator 1220, whiles the sidesof 1233 and 1234 away from the log amps join at node 1219, connecting tothe non-inverting input of comparator 1220. The output of 1220 on node1230 feeds back via large resistor 1241 to give a small regenerativefeedback to the non-inverting comparator input, giving clean switchingbetween high and low states of the drive signal on 1230, indicated bytrace 1240 labeled “Vd:” and representing the variable-duty-cycle drivepulse train going to the gate of FET 1242. The log comparison imbalancethus generates an oscillation at variable duty cycle that dynamicallybalances the equations and causes the square of flux, generating force,to track the PID motion equation very tightly after a typical initialperiod of stewing when a circuit is first activated. Completing thecircuit, computer 1223 provides output on bus 1224 to set thedigital/analog converters 1225 and 1227. Two single-bit digital outputfrom 1223 on lines 1225 and 1227 couple via two pairs ofseries-connected diodes, 1226 for the pair from 1225, and 1228 for thepair from 1227. Current can flow in the anode-to-cathode directionthrough pair 1226 from 1225 to 1218 and the inverting input of 1220, sothat a high logic level on 1225 will overcome the forward bias thresholdof the diodes and push the inverting input positive, forcing thecomparator output low. Similarly, a high logic level on 1227 will forcethe non-inverting comparator input positive, forcing the comparatoroutput high. Thus, computer 1223 can force the initial launch of thesolenoid. A potential problem arises if the feedback circuit, underslewing conditions, keeps Vd low, and the drive transistor turned off,for too long, for then the sampling of the position sense signal on 1210is interrupted. A train of short pulses from computer output 1227 canenforce a minimum frequency of sampling updates, keeping the feedbackloop closed.

Pot Core Solenoid With Flat Spring Suspension

FIG. 13 illustrates the mechanical configuration of a solenoid based ona standard ferrite pot core and a flat spring suspension that holds veryprecise parallel alignment of the pot core pole faces. Ferrites have thedesirable property of high resistivity, avoiding the confusing effectsof eddy currents that present problems to servo control. Powdered ironcores are also useful, as are cores built of thin laminations of tape,whereas solid iron solenoid cores present eddy current problems. Wheremagnetic force is to be maximized in a small space, the highersaturation flux of metallic iron is desirable, but where efficiency issought, oversizing a solenoid core yields good efficiency and provides agood setting for ferrite use.

FIG. 13 shows the flat spring of the design in plan view at 1320 on theupper left, the solenoid assembly in elevation section in open andclosed positions at 1300 and 1310 on the bottom left and right, and incutaway perspective, also in closed position, at 1315 on the upperright. File core halves, labeled in view 1300, are stator 1301 andarmature 1302, the stator bonded into cylindrical housing 1380 and thearmature clearing inside 1380 while bonding to core 1340. The cores areillustrated with a gap at 1300, and in the energized, fully closedposition at 1310. The suspension for the solenoid uses two identicalflat springs, illustrated at 1320 and consisting of an outer ring 1326for mounting in a housing, an inner rectangle 1325 with a center hole1329 for shaft mounting, and two “staircase” sections 1327 and 1328placed symmetrically on either side of region 1325. Each “staircase”section consists of two parallel strips which both terminate on the sameside, e.g. in the case of 1327, terminating on the left into 1326 and1325, while the two strips join each other at the stairway landing,”e.g. on the right in 1327. Axial displacement of 1325 relative to 1326causes the two “stairway” sections to form S-shaped sloping curves(relative to a flat in-plane reference) while the cosine-factorshortening of the flat projection of the sloping “stairway” sectionscauses the “stairway landing” section at the junction of the two stripsto pull in, while the ends of the paired strips make attachment tosections 1326 and 1325 following pure axial motions. The staircase shapejust described is viewed in 1310, specifically at views 1322 and 1324 ofthe springs viewed edge-on flat at 1321 and 1322. Perspective view 1315aids in visualizing the bend of spring 1324 in three dimensions. Observethat screw cap 1331 of-view 1300 is seen pushed further upward in 1333of view 1310, providing thrust actuation to an external load. Anextension from screw cap 1332 could be provided for pull actuation. Whenthe spring is not too extended beyond flat, it has very high rigidityagainst in-plane movement of the center relative to the perimeter, whilecompliance to axial motion can be made comparatively high and quitelinear.

Observe that all the bending in the spring described here is “planar” or“cylindrical,” meaning that local curvature is always tangent to somecylinder whose axis is parallel to the original flat plane. This is incontrast to a flat spiral spring, which is forced to twist with largeaxial perturbations unless each loop of the spiral makes a full 360degree are (or multiple 360 degree arcs) between inner and outerattachments. A thin strip of metal is much stiffer in torsion andin-plane bending than in cylindrical bending. In a flat spiral spring,the initial bending with small departures from a flat plane takes theform of cylindrical bending, since that is the “path of leastresistance.” At large axial perturbations, as the cosine of the slope ofthe spiral arms becomes significantly less than 1.0, the center sectionof a spiral spring is forced to rotate, which in combination with theaxial displacement results in twisting and in-plane bending of the flatspring. The overall result is a nonlinear increase in axial force. Bycomparison, the spring illustrated here does not tend to rotate withaxial displacement and has a significantly larger linear range than acomparable spiral spring.

Screw cap 1332 clamps the inside of the lower spring 1322 to core 1340,while lower housing cap 1312 clamps the perimeter of 1322 to the lowerinside of outer housing 1380. Similarly, screw cap 1331 clamps theinside of upper spring 1321 to core 1340, while upper housing cap 1311clamps the perimeter of 1321 to the upper inside of outer housing 1380.Rigid parallel alignment of the pot core halves is important, since theslope between the mating surfaces results in an asymmetric concentrationof magnetic flux and force, accentuating the departure from parallelalignment if the guide is not rigid. To establish precise parallelism atclosure, one method is to allow for some slop at the outer perimeters ofthe springs, then to fill the outer clamp areas with adhesive, then toforce the core halves together so that they are necessarily parallel,and finally to cure the adhesive (e.g., using ultraviolet Curingadhesive), Fixing the springs in their intended final positions as thecore halves mate.

The windings for the solenoid are indicated in views 1300 and 1310 byschematic “X” shapes for winding cross-sections, with thick innerwinding 1360 and thin outer winding 1370 Filling bobbin 1350. View 1315shows the cut ends of the wires. The thick winding would typically bethe drive winding, and the thin winding the sense winding, if a sensewinding is required by the servo circuit chosen. View 1315 does not showcertain details, e.g., the threading of end caps 1331 and 1332 intocentral shaft 1340, the three components appearing as a single cutawayobject in view 1315. Note that end caps 1311 and 1312 of view 1300 areshown with an annular center section cut out for view 1315.

Volume-control Pump Using Solenoid Actuation and Measurement

FIG. 14 illustrates a complete fluid pumping and precision volumecontrol system based on three servo-controlled solenoids: one solenoideach for inlet and outlet valving, and one solenoid for pump actuationand measurement of volume and volumetric compliance. The compliancemeasurement is useful for quantitative detection of bubbles in thepumped fluid.

The inlet valve solenoid at 1430 and the outlet valve solenoid at 1440are like the solenoid illustrated in FIG. 13 except for two things: theactuation ends that were shown at 1331 and 1333 have been flattened atthe tips of equivalent end caps 1401 and 1403 to lie flush with the tophousing surface in the unenergized or retracted position, as shown onthe left with 1401 of assembly 1430; and the suspension springs arepreloaded differently, so that the spring are flat and relaxed with thesolenoid is closed, as discussed below. Like 1333, 1403 is shown in theenergized and fully extended position. The pump solenoid at 1410 is ascaled-up version of the valve solenoids, except for modifications toact as a modified pull solenoid, the modification being a suspensionbias to push less, rather than pull, when energized. Screw and cap 1402,the counterpart of 1401 and 1403 of the valve solenoids, is used in1410—to retain the flat spring at its end of the suspension, and to holdmagnet holder 1480, which as described earlier (in relation to FIG. 9A)retains magnets 1482 and 1484. Those magnets work in conjunction withHall effect device 1486 as a displacement sensor, as discussed. Cap1404, the counterpart of 1332 of FIG. 13, extends into a foot thatpushes on a rubber dome 1415, which is part of larger molded rubbercomponent that includes valve domes 1414 and 1432. In its relaxed shape,this dome has a nearly hemispheric shape, but when cassette 1400 isloaded into place between the actuator solenoids, the dome is compressedby 1404 as shown.

The pumping and fluid metering action to be described below is similarto the operation of the invention described in Applicant's U.S. Pat. No.5,624,409, “Variable Pulse Dynamic Fluid Flow Controller,” sharing withthat invention the use of valve timing synchronized to the naturalperiodicity of fluid flow into and out of a container having fluidvolume compliance, so that flow can be maximized in a resonant pumpingmode, or controlled in very small-volume fluid pulses utilizing acombination of valve timing and fluid inertia to give a non-linear flowregulation affording a very wide dynamic range of delivered pulsevolumes. The operation described here shares the fluid volumemeasurement function described in U.S. Pat. No. 5,624,409, except thatin the invention described here, the measurement device doubles as theactuation device, i.e. the solenoid, in an active pump. The system ofU.S. Pat. No. 5,624,409 was conceived as a passive metering devicereliant on fluid motive force from a pressurized fluid source, unlikethe active system described here.

When solenoid 1410 retracts, pulling foot 1404 back from the positiondrawn, the preload in the rubber dome generates a negative fluidpressure in the fluid beneath the dome, here shown as continuous throughthe outlet valve area on the right, around 1416, and continuous with theexiting fluid indicated at 1450 (fluid connections to the right of 1450not being shown). Thus, in an inlet stroke, the valve on the right isclosed and the valve on the left, around 1422, is opened, 1410 isenergized, 1404 retracts and relieves the downward force on 1415, dome1415 responds by expanding upward toward its original molded shaped andgenerates a negative pressure underneath, drawing fluid in from theinlet fluid at 1420 (fluid connections to the left of 1420 not beingshown). Typically 1404 retracts faster than inlet fluid can follow, andthe pump solenoid soft-lands under servo control and holds near closurefluid comes through the inlet to fill in under dome 1415 and allow thatdome to catch up with foot 1404. With optimum timing, the valve around1422 closes just as the kinetic energy of incoming fluid has paid outfully in fluid volume overshoot and flow has come to a complete halt.One timing method causes 1410 to be de-energized a few millisecondsbefore the inward fluid flow through the inlet valve has come to a halt,at which time 1410 is retracted with its magnetic gap as close aspractical to full closure and mechanical contact, i.e. hovering underservo control at a minimal gap. The springs In 1410 at this pointresemble the springs illustrated for solenoid views 1440, 1310, and1315. As the current and magnetic field decay in 1410, the decay ofmagnetic force ceases to counterbalance the downward spinning force, sothat foot 1404 would be inclined to start dropping. With proper timingin relation to the momentum of incoming fluid, however, the buildup offluid pressure under dome 1415 will roughly counterbalance the increasein downward force on 1404, so that as fluid flow comes to a halt, fluidpressure will reach its maximum in balance with the suspension springsof 1410, and 1404 will barely move during the final decay of solenoidcurrent and synchronized buildup of fluid pressure. The drive to 1430 isremoved in anticipation of a slightly delayed mechanical response bringabout fluid shutoff at just about the moment when fluid flow stops andwould reverse if the valve were to remain open.

Bubble detection can proceed at the end of a fluid fill stroke, whenboth valves are closed, by at least two distinct approaches. By a“static” approach, a high impedance solenoid current source circuit,such as is illustrated in FIG. 10 around amplifier 1090 and transistor1099, is used to halt the decay of solenoid current and hold current ata steady level, resulting in some magnetic closure force, reduced forceon foot 1014 (as compared with the zero-current force), and thereforereduced initial fluid pressure under dome 1415. A ping measurement thendetermines the effective magnetic gap X of 1410. Solenoid current isthen altered, e.g. reduced to zero, and a second ping measurementdetermines the new position X at the new force and fluid pressure. Thechange in X from the one measurement to the next, for a change of forcethat is readily calculated from the current levels and ping frequencies,is a measure of compliance of dome 1415 and the fluid underneath. Withbubble-free fluid, there will be a normal, low compliance associatedwith stretch in the rubber dome, which by design is relatively thick andwhose unsupported annular area outside the contact of 1415 is, bydesign, roughly the surface of revolution of a circular arc, thusdescribing a slice out of the top of a circular torroid, a shape thattends not to be deformed by fluid pressure. If bubbles are present inthe fluid, the compliance of the dome will be measurably increased,indicating the approximate total bubble volume. By a “dynamic” bubbledetection approach, solenoid drive winding current in 1410 is forcedrapidly to zero at the end of the fluid inlet cycle, e.g. by use of azener diode “braking” circuit such as is illustrated in FIG. 10 anddescribed earlier in relation to the operations of optical switch 1088and series diodes 1097 and 1091, the latter being the zener diode. Thesudden removal of solenoid current causes solenoid foot 1404 to fallinto the fluid filled cushion of dome 1415. The dynamics of theresulting short drop and bounce provide a clear indication of gasbubbles captured in the liquid chamber. With no bubbles, the dome willcompress comparatively little, causing the solenoid to rebound quicklyinto a comparatively high frequency transient oscillation. Bubbles willallow the dome to compress more and rebound more slowly into alower-frequency transient. Detection of the transient can be observed invarious ways. If the Hall effect motion sensor is implemented as drawnin FIG. 14, digital sampling of the Hall sensor output will record thetransient for analysis. Another approach is the dynamic analysis of anindicator-capacitor ping transient, using a circuit like that of FIG.10. By opening switch 1088 to bring the zener braking into play, andmore or less simultaneously closing switch 1087 to bring ping capacitor1063 into play, current will stop and a ringing transient will occurstarting just as the downward spring force on 1404 reaches its maximumwith the removal of opposing magnetic attraction. The transient bouncebehavior of the solenoid will be reflected as a frequency modulation inthe electromagnetic ringing response of the solenoid inductor-capacitorcircuit. This oscillation may be monitored via ADC interface 1040 ofFIG. 10.

Once inlet fluid is captured under dome 1415 and ping measurements haveperformed any needed bubble checking and determined a resting positionmeasurement of X and, by calibration, the associated fluid volume, thenfluid can be released via the valve around 1416 and through the port at1450 to delivery tubing and a delivery site not shown. As described inApplicant's U.S. Pat. No. 5,624,409, fluid can be released in smallpulses or in a maximum-volume bolus, with the outlet valve opening timedto last for approximately on half the natural oscillation period of theoutlet path, taking account of fluid inertia and compliance particularlyof the volume under 1415 coupled with the spring suspension of 1410.Depending on tubing length and diameter and the nature of thefluid-receiving load, there may be significant overshoot to theexpulsion of fluid from under 1415. FIG. 14 illustrates an unloadedsolenoid position of 1410 that would be observed at the end of aresonant half-cycle fluid expulsion, when the suction generated by fluidovershoot has pulled a negative pressure under 1415 and caused that domealmost to break contact with foot 1404, leaving the suspension springsin 1410 fully unloaded and flat, as drawn. Under most operatingconditions, foot 1404 will be pushed upward to some degree by acombination of elastic forces in dome 1415 and fluid pressure beneath1415, with the metal spring suspension providing a counterbalancingdownward force. It is helpful to consider dome 1415, with its springrate and preload, as an integral component of the mechanical suspensionof 1410. Thus, at equilibrium with zero fluid pressure, 1404 is pushedupward somewhat from the position illustrated and a preload in the flatmetal springs of 1410 is balanced against an opposing preload in therubber of dome 1415.

Examining fluid cassette 1400 in more detail, small rubber dome 1414 onthe left is similar to dome 1415 except that its convex surface facesinward to the contained fluid, as is the case with similar dome 1432 onthe right. The three domes are clamped between upper plastic housingpieces 1413 and 1412, which are continuous across the top of thecassette from the far left to the far right, even though holes in theplastic lying at the plane of the elevation section view cause thesections of tipper housing to appear to be discontinuous. The differenthatching pattern on 1413 and 1412 shows which parts viewed in sectionbelong to which whole piece of plastic. Observe that piece 1412 forms acircular ridge coming up under the annular bulge in dome 1414, andsimilarly under dome 1432 The right hand circular ridge is seen to beseparated from dome 1432 at the gap indicated by 1460, and around thatperimeter. Thus, the right hand valve is shown open. All fluidcontiguous with 1420 is hatched with vertical dashes, while fluidcontiguous with 1450 through the opened outlet valve is hatched withhorizontal dashes. Observe that this outlet fluid is continuous aroundthe outer perimeter of dome 1414, being seen in all only apparentlyisolated area just below and to the left of 1414. Bottom plastic piece1411 of cassette 1400 is bonded to 1412 out of the section plane of thefigure and, in the viewed section, just below the inside edges of thecircular valve ridges, supporting the ridges at the part of theirperimeter where a gap in 1412 allows fluid flow to communicate from theouter perimeters of domes 1414 and 1432 into the central fluid reservoirunder dome 1415. A valve actuation linkage is seen formed in piece 1411at pusher cycle cylinder 1422, which is field up against dome 1414 byforce exerted from cap 1401 of the inlet valve solenoid. The thincurving annulus 1418 makes a flexible rolling seal for permitting axialmotion of plug 1422 while maintaining a fluid seal. This flexing seal iscomparable to the shape found around the perimeters of audio loudspeakercones. On the right, cylinder 1416 is seen pushed up by actuator cap1403, and the deformation of the flexible seal around the bottom of 1416is evident by comparison with 1418. The upward thrust of 1416 is seen tounseat the ring or contact between dome 1432 and the circular valveridge formed in piece 1412, opening the valve. The valves are heldclosed by preload in the rubber of dome areas 1414 and 1432, pushingdown on the circular ridges. Thrust cylinders 1422 and 1416 are alwayspushing upward when the cassette is loaded in contact with the valveactuators, as indicated by the stretching of the flat spring in solenoid1430. Energizing a valve solenoid adds magnetic force, increasing thatupward thrust and caving the dome center sufficiently to cause anannular opening around the circular ridge seal. When the cassette isremoved from contact with the valve actuators, cylinders 1422 and 1416are pushed down by rubber domes 1414 and 1432 until, at maximumextension, the rolling seal sections at 1418 and the comparable sectionon the outlet side are stretched into conical surfaces extending down,with little preload remaining in the valve domes. Thus, it is seen thatcoupling the cassette to the valve actuators moves the valve domes to ashape, in dynamic balance with the valve actuator spring, partway towardopening, so that a relatively small magnetic thrust force and smallmotion suffice to open a valve. The first fraction of the poweredsolenoid thrust, e.g. the first third, stretches the dome, while thesecond fraction of travel opens the valve. The gap opened up, e.g. at1460, is less than the second fraction of solenoid travel, e.g. half ofthat second fraction, so that by this example, a total valve thrust of0.024 inches would initiate valve opening after 0.008 inches, and overthe next 0.016 inches of actuator travel the valve gap would open by0.008 inches, quite sufficient for flow in a medical disposable.

The effect of fluid pressures on valve operation in cassette 1400 is asignificant issue for smooth operation without sudden closure andcavitation. The effective displacement areas subject to force from fluidpressure are preferably matched between flex area 1418 and fluid-exposeddome area 1414, and comparably for the flex area opposing dome 1432.Dividing pressure effects into differential pressure effects, related tothe pressure difference across a valve, and common mode pressureeffects, related to the average of the pressures on either side of avalve, the intent of this design is to minimize the effect of commonmode pressure. An increase in common mode pressure pushes down oncylinder 1422 via pressure excited on 1418, but the pressure partiallyunloads the dome force whereby 1414 pushes down on 1422. Thus, a changein common mode fluid pressure has only a minor effect on actuatorposition. When a valve, e.g. the inlet valve, is closed, thedisplacement area on the inner annulus or 1414 is less than thedisplacement area at the same pressure on 1418, so that a positiveincrease in inlet fluid pressure from 1420 would tend to push 1422 down,keeping the valve closed. A negative pressure communicated from thevolume under dome 1415 would reduce the upward force on 1414, againtending to close the valve. Thus, a differential pressure going positiveto negative from inlet to pump chamber tends to close the inlet valve,and conversely, an outward-directed pressure differential tends to openthe inlet valve. The valve can thus be compared to a fluid diode with arelatively low forward cracking pressure and a much higher crackingpressure, associated with the total positive pressure tending to cavedome 1414 in and cause the dome to lose contact with thrust cylinder1422. If the inlet valve is thrust open by solenoid actuation and beginsto close in the presence of fluid flow, it will tend to slam shutabruptly as an increasing pressure differential across the closing valvedrives the valve toward further closure. This regenerative closureaction is absent for flow in the opposite direction, from pump chamberto source, since the developing pressure differential across the valvetends to keep the valve open. The outlet valve performs similarly,tending to close smoothly, providing a continuous braking action tooutward fluid flow as solenoid actuator force is reduced. Recalling theresponse of the servo circuit of FIG. 10 to the control signal “OPEN” at1011, it is seen that a ramped reduction of electromagnetic force onsolenoid 1440, generated when logic level “OPEN” goes high, will resultin a smooth throttling of fluid flow, avoiding water hammer andcavitation effects with the dome valve discussed here (as contrasted,e.g., with a tube pinch valve, which tends to self-close abruptly.) Inintended operation of the fluid flow control system of FIG. 14, usingcontrol strategies described in detail in Applicant's U.S. Pat. No.5,624,409, a common operating procedure is as follows: 1) perform a pingmeasurement on 1410 to determine initial fluid volume in the pumpchamber; 2) apply power to pump actuator 1410, initiating a decrease influid pressure in the pumping chamber below dome 1415; 3) possiblybefore or possibly after step 2 in temporal sequence, depending onresponse delays, apply power to valve actuator 1430, so that valveopening will commence at about the time that pumping chamber pressurebefore inlet pressure; 4) allow actuator 1410 to approach magneticclosure under servo control; 5) allow enough time for fluid flowacceleration and deceleration that dome 1415 begins to catch up withfoot 1404; 6) remove power from 1410 just in time to prevent fluidmomentum from causing this actuation solenoid to be bumped closed, whichwould otherwise cause, an audible click; 7) possibly before or possiblyafter step 6 in temporal sequence, depending on response delays, removepower from 1430 early enough that fluid closure will be reached just asflow through the valve is reversing; 8) perform a ping measurement with1410 to compute fluid volume, subtracting the volume from step 1 inorder to update the long-range cumulative estimate of delivered volume;9) energize valve actuator 1440 for a predetermined pulse interval,allowing some fluid to exit the pumping chamber; 10) repeat the pingmeasurement of remaining fluid volume, compute the delivered volume, anddetermine a correction for a subsequent outlet valve pulse, if calledfor; 1) repeat steps 9 and 10 zero or more times, to complete the fluiddelivery cycle.

The sequence just described is modified according to desired fluiddelivery rate and current progress relative to the time-varying targetfor total delivered fluid. Long-term cumulative volume is always basedon volume difference from just before to just after an inlet stroke, sothat uncertainties of long-term drift in the volume estimation areminimized. For a high delivery rate, a maximum volume intake is followedby a maximum volume delivery, each with a flow pulse timed to thenatural half-period of oscillatory flow on the inlet or outlet side(unless, e.g., the outlet flow dynamics are more than critically damped,in which case the “ideal” outlet flow pulse interval is less welldefined.) For a lower delivery rate, the outlet flow pulse isinterrupted by valve closure in early to mid course, before a maximumvolume has been delivered, and the fluid energy available from the pumpchamber, amounting to spring energy stored in the suspension of 1410, ispaid out over two or more pulses. It is in this form of operation thatsmooth release of the valve actuator, and inherently smooth,non-regenerative action of the fluid valve, are essential to quietoperation without cavitation bubbles.

In addition to the operating modes just described, a “firehose”operating mode is possible with the hardware of FIG. 14. Ideally theinlet fluid connection from 1420 has a low impedance, both lowresistance and low fluid inertia, so that fluid can be drawn in quickpulses. The outlet connection from 1450 typically has a much higherimpedance, including the substantial inertia of fluid in along tube.Consequently, the natural period for fluid oscillation involving inertiaand the spring rate of the pumping chamber is much slower for the outletside than for the inlet of the pump system described here. Firehose modepumping begins with a fill pulse, as described in steps 1 through 7above. The outlet valve is then opened and maintained open continuously.As the pump chamber begins to be depleted and fluid pressure isdropping, refill steps 1 through 7 are repeated while outlet flow isongoing. With sufficient momentum in the outlet line, the negativepressure spikes to pull more fluid into the pump chamber will not lastlong enough to halt the outlet flow, so that continuous flow will bemaintained as the inlet and pump valves cyclically recharge the pumpchamber. Volume cannot be tracked as accurately in this mode, sinceinlet and outlet flow overlap in time. Volume can be estimated from thedynamics of pumping performance. In typical medical infusionapplications, volumetric measurement and control are of secondaryimportance when a maximum rate delivery mode is invoked.

Low Power Hovering/Levitation Servo Using Permanent Magnets

FIG. 15 illustrates a modification of FIG. 9 to use permanent magnetsfor maintaining solenoid position hovering near closure, exertingcontinuous magnetic force with near-zero power consumption. Asingle-point hanging levitation system could share the same electronicconfiguration. A two-point or multi-point levitation system could usetwo or multiple copies or the electronics, one for each independentdegree of freedom of the suspension. The comparator 790, NOR gate 720,and switching transistor 730 inherited by FIG. 9 from FIG. 7 arereplaced in FIG. 15 by power amplifier 1504, whose output stage isdesigned for a switching output voltage able to swing very close toeither the positive or the negative supply rail. Amp 1504 is designed tobe turned off when the center input 1505 between the inverting andnon-inverting inputs, labeled “0,” is driven high by the “Off” signal752 originating in FIG. 7. This shutoff function parallels the NORgating function first introduced in FIG. 7 at 720. The bipolar amplifieroutput is required so that line 1507 to the drive coil can go on eitherside or the ground reference provided on the other side of the coil, at1503, which in FIG. 9 was a positive power supply connection. A currentsense resistor and associated differential amplifier are as in FIG. 9.

The primary difference between the system of FIG. 15 and that of FIG. 9is the inclusion in solenoid assembly 1500 of permanent magnets at 1501and 1502, on the pole faces where the magnetic flux loop closes. Thesemagnets are symbolized by small arrows in the direction of poling. Asfar as dynamic inductance is concerned, permanent magnet material has arelative permeability (compared to vacuum) generally between 1.0 and1.20 (excepting for Alnico magnets, whose relative permeability is muchhigher), so the effective dynamic inductance gap X is drawn at 1510 toinclude most of the thickness of the permanent magnet material, as ifthat material behaved inductively almost like air. The other effect ofthe magnet material is to add the equivalent of a DC bias currentflowing through the drive coil. If this equivalent bias current iscalled “lo” as in 862 of FIGS. 8 and 9, then a sensed current of zero atthe sense resistor and differential amplifier will be equivalent to acurrent of lo in the earlier context. Thus, the bias potential to theintegrator non-inverting input at 1508 is set to zero, i.e. groundpotential, instead of Io as at 862 of the earlier circuit. With thesemodifications, the control circuit seeks out the gap X for whichmagnetic force is in balance with mechanical load force at zero averageoutput current. At circuit equilibrium, for symmetric positive andnegative supply voltages the output from 1504 on 1507 will be a squarewave at 50% duty cycle. The current will resemble a triangle wavefluctuating about a zero average, and most of the supply current drawnduring part of a conduction cycle from a given supply (positive ornegative) will be pumped back into that supply by inductive action overanother part of the conduction cycle. Thus, the power drawn formaintaining hovering or levitation will be the low power necessary tokeep the electronic circuit “alive,” to overcome AC magnetic losses andtransistor losses associated with switching and the maintenance of a lowlevel current ripple, and to provide perturbations in magnetic force forcorrecting position errors.

The increased value of effective gap X arising from the inclusion ofpermanent magnets implies that more coil current must be used to varythe magnetic field than would be required if the permanent magneticmaterial were filled with a high-permeability transformer-type ofmaterial. If the major power requirement is for static holding, thenusing a permanent magnet to offset DC electric power is well worth thesacrifice in AC efficiency. In a magnetic propulsion system to beexplained below, however, large AC field variations are employed toeffect propulsion, as the steady DC work of lifting is taken over bypermanent magnets. To minimize AC power consumption in such allapplication, the permanent magnet material should be configured, in thegeometry, to be thin and spread out over a wide area, so as to offer alow dynamic reluctance to the magnetic path, where reluctance varies asthe ratio of-length along the magnetic path divided by area. Thisgeometric proportioning implies that the permanent magnet material willoperate at a low permeance coefficient, which is equivalent to sayingthat the material will experience a high steady demagnetizing H-field.The factor for increased AC current needed to generate a given AC fieldstrength, due to the addition of permanent magnet material, is givenvery roughly by 1+Pc, where Pc is the steady permeance coefficient atwhich the permanent magnet operates in the magnetic circuit. The highestenergy product for a permanent magnet is obtained at a Pc of about 1.0,implying a doubling of AC current and a quadrupling of AC power for agiven AC flux excitation, compared to operation with no permanentmagnet. Most permanent magnets are operate at a Pc greater than 1, butin contexts to be described for magnetic levitation and propulsion,values of Pc of 0.5 or less are desirable. While a low Pc implies a highsteady demagnetizing H-field, the application of AC coil power willcause higher peaks in the demagnetizing H-field, driving the net flux inthe permanent magnet material dynamically to nearly zero. The materialchosen for such an application must necessarily have a high coerciveforce so that the material will not be depoled by the stresses ofoperation. Furthermore, for a relatively thin layer of permanent magnetmaterial to be effective at generating a field bias, the material musthave a high poling strength, which amounts to saying that the residualB-field, Br, needs to be high. The highest available energy-productNeodymium Iron Boron magnet materials have high Br, exceeding 1 Tesla,but not a high enough coercive force to operate at very low permeancecoefficients, with additional AC field variation, without significantloss of strength. Formulations optimizing high coercive force are to besought for good performance under the conditions described. The amountof material required will exceed the minimum that would merely producedthe needed lifting force over a given gap, if the design is furtheroptimized for efficient AC performance. These expense compromises will,however, pay off richly in achievement of a very efficient lifting andpropulsive magnetic motor, as will be seen.

Note that the modifications to the circuit of FIG. 9 for inclusion ofpermanent magnets apply similarly to modifications to the circuit ofFIG. 12. One need only provide for bipolar current drive, set the targetgap to an estimate of the zero-current gap, and effect integral feedbackthrough the computer interface to dynamically re-bias the systemparameters to achieve the zero-current gap. An analog integrator canalso replace the microprocessor loop.

Servo for Symmetric Landing

The servo systems described above control one axis of motion. Theinherent instability of magnetic alignment has been noted, and a springsuspension system for rigid alignment control has been described. Onecan correct the alignment of an object by the same techniques used tocontrol position, sometimes with simplifications over the general servocontrol problem. Consider a solenoid fabricated from standard “E-I” coreparts, where the E-core is the stator and the lighter 1-core is thearmature, drawn to the E-core. As the 1 approaches the E, any tiltplacing one end of the 1 closer to the E than the other end will cause aconcentration of magnetic flux across the narrower gap. For smallalignment errors and no core saturation, the destabilizingmagnetic/mechanical spring rate is given roughly by the total force ofattraction between the E and the 1, multiplied by the cube of thedistance between the centers of the center and end mating surfaces ofthe E, and divided by the square of the average gap. Thisdestabilization can overcome very stiff suspensions near closure.Magnetic alignment correction becomes more precise as the gap becomessmaller, with no singularity in the servo loop as the gap approacheszero if the total magnetic force is also under control.

Consider an E-core with two pairs of windings: a force drive and forcesense winding wound around the center prong of the E, and all alignmentdrive and alignment sense winding on each end prong of the E, the endwindings being wired in series so that current flow is in the oppositerotation sense at either end, as with current going around a figure-8loop. Thus, after interconnecting the alignment windings, one has a pairof drive leads and a pair of sense leads coming back to the electroniccontroller, as with an ordinary drive and sense winding. The signal fromthe sense winding represents the rate of change of flux imbalancebetween the ends of the E, and the time integral of that signalrepresents the total flux imbalance. Merely shorting the asymmetry drivewinding causes an electromechanical damping of the kind of rotation ofthe 1 relative to the E that generates unequal gaps, while shorting asuperconductive figure-8 winding around the ends of the E. would almostcancel the destabilizing torsional force. The circuit of FIG. 15 call beused in a symmetry-maintaining servo, accomplishing roughly the functionof a superconductive loop, and more. In FIG. 15, the feedback signalcomponent “Prp1” originating from integration of the sense coil outputvoltage accomplishes roughly what a superconductive figure-8 windingwould do: to generate a steady current in response to a change inmagnetic flux, whose current direction is such as to cancel that changein flux. While this function fights the basic instability, the dampingdifferentiation loop aids fast settling, and the integration of thecurrent signal provides the feedback that drives any residual asymmetrycompletely to zero: only with a flux balance will no current be requiredto prevent armature rotation.

If conditions at the start of gap closure are nominally symmetric, i.e.when the initial asymmetry is small and unpredictable, then the bestguess for the DAC output in FIG. 15 is zero. Thus, the DAC and itsoutput resistor may be eliminated for most symmetry applications.

While a circuit of the topology of FIG. 15, or simpler, can be used tocorrect angular misalignment about one axis, two such circuits cancorrect angular misalignment about two axes, bringing two solenoidcomponents together completely flat. Consider replacing the straightcross-piece of an I core with a “+” shape, and replacing the E core witha “+” having four square prongs extending from the tips of the “+”shape, like two E-core shapes on their backs, perpendicular andsuperimposed. A pair of symmetry servos can accomplish parallel hoveringand “four-point landing” as mentioned early in this paper.

System for Levitation and Linear Propulsion

The principles illustrated above find potential applications inheavyweight lifting, e.g., of a levitated monorail car suspended below atrack. When a long object is suspended from a narrow rail, atwo-variable suspension servo is required, to keep the car up and tokeep it level from front to back. To provide fore and aft propulsivethrust and braking, the shape of the lower surface of the track ismodified to include periodic waves of vertical ripple, varying theheight of the track with variation in longitudinal position. Waves ofvariation in magnetic field strength are generated within electromagnetsand their associated control modules arrayed along the length of thecar, those waves being caused to travel backwards along the car at avelocity that synchronizes the waves that travel with respect to the carto the stationary vertical ripples in the track, so that a given portionof the track sees a relatively constant magnetic field strength duringthe passage of the car. Control of the phase and amplitude of the wavesin magnetic field strength with respect to the waves of vertical ripplein the track will result in control of thrust or braking.

The suspension problem can be approached as two independent servos forthe ends of the car, or as a levitation servo for common mode controland a symmetry servo for differential mode control. In either case,individual electromagnetic control and actuation modules, receivingindividual flux-target inputs and providing individualposition-indicating outputs (or current-indicating outputs, sincecurrent required to achieve a given magnetic flux is related toposition, or magnetic gap), are controlled as groupings of inputs andoutputs. Separate groupings control different degrees of freedom of themotion of the car, e.g., vertical height, fore and aft pitch angleerror, and thrust or braking force. A generalized “position” signalassociated with a degree of freedom of the motion of the car isrepresented as a weighted average or weighted sum over a grouping ofcontrol and actuation modules. Weighted sums applicable to the geometryof the suspension drawn near the top of FIG. 16 are: a set of similarpositive weightings to indicate vertical height; a set of weightingsvarying from positive at one end of the row of actuation modules tonegative at the opposite end of the row, to indicate fore and aft pitchangle error; and two sets of weightings varying periodically betweenpositive and negative values, matched to the wavelength of the periodicvertical ripple along the longitudinal dimension of the track anddiffering in phase relative to the track ripple by 90 degrees, toindicate the sine and cosine components of position of the modulesrelative to the track ripple. (The circuit schematic of the lower partof FIG. 16 implements a slightly simpler thrust approach, based on trackslope measurements between pairs of modules straddling a given module,rather than on a sine/cosine reduction across the entire set ofmodules.) Associated with a given weighted sum of position indicatingsignals relating to a given control degree of freedom, is a set of servooutput signals associated with the same degree or freedom. In the caseof magnetic wave generation for thrust or braking, differing componentsof an Output signal set will generally contain different phaseinformation. Outputs to control a positioning or alignment degree offreedom will generally represent separate weighting factors of a singlescalar value, that scalar being the input weighted sum. The geometricpattern of output weightings typically resembles the pattern of inputweightings, e.g. equal input and output weightings for lift, orweightings varying linearly with position for pitch angle control.

With active control of elevation and pitch, the degrees of freedom oflateral translation, yaw, and roll come to be regulated passively. Ifthe fore and aft suspension magnets tend to self-center laterallybecause of their geometry, then lateral translation and yaw will bepassively stable. For an object hanging below a track, gravity controlsroll. For high speed operation of a rail car in wind and roundingcorners, very effective damping of roll (i.e. of swinging below therail) can be provided by active aerodynamic fins. Fore/aft position isnot controlled in the static sense, being the direction of travel, butthrust and braking may be controlled by synchronization of travelingwaves of magnetic flux to the waves of vertical height along thelongitudinal dimension of the track, as explained above.

To minimize magnetic losses due to hysteresis and eddy currents in thetrack as the levitated system moves at high speed, the liftingelectromagnets preferably generate fields laterally across the track,rather than fore and aft. The lifting electromagnets should abut eachother so that their fields merge into a fairly uniform field over asubstantial length of track, ideally over the entire length of themagnetic lifting system. The electromagnets cannot readily merge theirfields “seamlessly” along the length of the car (although geometries ofpermanent and soft magnetic materials could greatly smooth the field),for some magnetic separation is required to isolate the differentactuation signal strengths of the different magnets. The magnetic fieldinduced in any part of the track goes from zero to a maximum and back tozero just once during the passage of the levitated car. The slightseparation of the magnet sections will inevitably cause some ripple infield strength in a given part of the track during passage of the car,but large fluctuations and total field reversals are to be avoided.

If the magnetic flux were to travel longitudinally in the track, ratherthan laterally, then one of two undesirable situations would arise. Ifthere were no flux reversals in a part of the track during the passageof the car, that would imply that all the magnet poles on one end of thecar are North, while the poles on the other end of the car are Southpoles. Then a cross-section perpendicular to the track length of trackwould have to support the entire magnetic flux that lifts the car, asmust the cross-section of the magnetic flux return path through thelevitation system on the car. If the magnetic poles on top of the carwere to alternate between North and South some number of times along thelength of the car, this would cut down on the cumulative buildup oflongitudinal flux in the track but would also generate flux reversals inany given portion or the track during the passage of the car. Avoidingthe horns of this dilemma, FIG. 16 illustrates a suspension andpropulsion system that induces primarily vertical and lateral magneticfields in the track. The illustrated design offers several advantages.First, the design minimizes the track volume transmitting flux. Second,by avoiding a left-right magnetic dipole and using instead using asymmetric dipole pair as illustrated, with flux traveling from center toleft and right, the design achieves a magnetic quadrupole, whosemagnetic field has a much shorter range into the environment than adipole-field. Third, the design minimizes temporal flux variation in anyportion of the track as the car passes, thus making it practical tofabricate the track from ordinary solid iron or steel, withoutlaminations to inhibit eddy currents and without special alloying orheat treatment to minimize magnetic hysteresis. While AC magneticvariation is minimized in the track, magnetic variation is quite high inthe motor magnets, whose fields must be varied in synchronization withvertical ripples in the track to produce thrust and braking. By design,demanding specifications for magnetic performance are moved away fromthe massive track investment toward a much smaller investment in motormaterials.

Returning to FIG. 16, a row of eight magnet sections, 1600, 1601, 1602,1603, 1604, 1605, 1606 and 1607, is shown levitated below track 1610 andaligned to that track. The track itself has the form of an I-beam whoseattracting bottom surface is modified by a lateral convex rounding andlongitudinal sinusoidal rippling, the rounding to allow for banking inturns and the rippling to be used for propulsion. That rippling is seenin the sinusoidal curvature of the track edge represented by line 1612.The illustration shows four magnet sections per wavelength of ripple inthe track, implying a four-phase propulsion motor A practical minimum ofabout three magnet sections per wavelength is desirable for smooththree-phase propulsion with low vibration, while a higher longitudinalsubdivision of the motor magnets per track wavelength results in lessripple of the magnetic field induced in any given portion of the trackas the levitating system passes by. Each magnet section in thefour-phase propulsion system illustrated consists of a ferromagneticcore piece and a winding, as labeled for the components of section 1607.The end of the core is seen as rectangular parts 1616 on the left, 1618in the middle, and 1620 on the right. These three parts are joined by abridge across the bottom middle region 1607, between the downwardbending lobes of the winding seen on the forward lobe side at 1622(viewed in perspective as nearer the viewer) and on the aft lobe side at1624, which abuts the forward lobe of the adjacent section at 1606.Middle core piece 1618 forms one magnet pole (north or south) whileouter sections 1616 and 1620 form the opposite pole (south or north).The winding is seen to loop around the center section to produce thismagnetic polarity differential, while the winding is bent down in theforward and aft lobes to allow for an unbroken surface along the topcore area of 1618. The downward bending of the winding also allows eachcenter section to abut its neighbor or neighbors on the ends. Theabutting core sections do not actually touch, but are separated slightlyeither in the middle or al the outsides or both, to inhibit longitudinalflow of magnetic flux, for two reasons: to inhibit longitudinal“sloshing” of magnetic flux toward regions of narrower magnetic gap withtrack 1610; and to avoid magnetic short-circuiting of the independentcoil drive sections, for pitch control and for generating propulsivemagnetic waves. Preferably, the separation gaps between core sectionsare small I enough, compared to the gap between the cores and track1610, that the gaps cause only minor traveling discontinuities in thefield strength induced in the track, while the gaps are also largeenough to avoid excessive unwanted longitudinal conduction of magneticflux.

While the motor sections 1600 through 1607 have been described as iflacking permanent magnet components, permanent magnets are readilyintegrated into the motor sections, thereby permitting cancellation ofthe DC component of electric current needed in the drive windings. Analternative motor section on geometry is illustrated in the upper-leftregion or FIG. 16, in the longitudinal elevation section indicated at01-01 by the dashed line with end arrows of the upper right of the twocross sections and actually viewed on the upper right, and in thelateral elevation section indicated at 02-02 by the dashed line with endarrows of the upper left of the two cross sections and actually viewedon the upper right. Curved lower track surface 1614 is the same for bothportions of the diagram and is therefore numbered the same, while thedetails of the motor section in two views on the upper left aredifferent. The side lobes 1616 and 1620 of the core viewed inperspective are replaced by lobes 1617 and 1621 of a U-shaped channelwhose relatively thin bottom section is seen at 1629 in both sectionviews. Bridging from the bottom of the outer U-channel to the centersection is a thin flat rectangular permanent magnet 1627, poled upwardacross the thin dimension as indicated by arrows. Following principlesdescribed above with reference to FIG. 15, (this magnet has a low ratioof length (along the poling direction) to area, and operates at a lowpermeance coefficient, with the result that the increment in AC magneticreluctance is kept low, in order to improve efficiency for generatingpropulsive magnetic waves traveling along the row of motor sections.Soft ferromagnetic component 1625 is seen to have a broad flatrectangular bottom for gathering flux from the permanent magnet andconcentrating that flux into an ascending cylindrical section, aroundwhich is placed winding 1623, a simple spool full of wire as contrastedwith the more complicated shape with bent-down lobes at 1622 and 1624.The flux from the top of the cylindrical portion of 1625 couples intorectangular center pole piece 1619, in which the flux spreads outlongitudinally before bridging vertically up to surface 1614 andcompleting the magnetic circuit by bridging vertically back down intothe sides of channel 1621. Observe the gaps between 1619 and itslongitudinal neighbor on the left, and similarly for the neighbors tothe left and the right of the comparable unlabeled motor section viewedin the middle of the group of three in longitudinal section. This gap isto retard unwanted leakage of flux between longitudinal motor sections.A gap is seen on the lateral left and right sides of magnetic conductorpiece 1625, this gap intended to prevent excessive short-circuiting ofthe permanent magnet flux to the lower part of 1621, since the desiredDC flux path is up through the winding and to bar 1619.

Calculations for practical vertical gaps to a suspending track (e.g.,fluctuating between one and three centimeters) and a practicallongitudinal wavelength (e.g., for 250 mile/hour propulsion with a trackripple wavelength on the order of 50 centimeters) and for a practicalpassenger car weight loading (e.g., on the order of 1000 pounds perlongitudinal foot of the suspension system) indicate that the fluxdensity bridging from the top of a component like bar 1619 to acomponent like surface 1614 of 1610, should be a comparatively smallfraction of the saturation flux for iron, i.e. a comparatively smallfraction of two Teslas. At higher flux densities, the concentration offorce becomes so great as to demand a lateral width of a motor yokepiece such as 1629 that is not much larger (or even smaller) than thedesired vertical gap to the track. For such a narrow lateral dimension,there is an excessive lateral leakage of flux, e.g., from 1619 directlyacross to 1617 and 1621, without much flux bridging vertically across tosurface 1614 and through part of 1610. To prevent lateralshort-circuiting of flux without generation of lift, the lateral widthof the motor cannot be too small in relation to the vertical gap, and byimplication, the upper surfaces or the motor need to operated at fluxdensities well below the saturation of iron. For maximum efficiency of adrive coil generating vertical lift corrections and propulsion, thecenter of the coil should be made as small as possible, so that theaverage circumference per winding is minimized. It therefore pays toconcentrate the flux from the broad flat bottom magnet of the figure upinto a small cylinder of magnetic material through the winding centerbefore the flux spreads out again at the top for travel across thevertical magnetic gap to the track. The cross-section of the windingcore should be made as small as possible, short of driving the peak fluxdensity up to the saturation level of the material. By making the bestsystem use of the permanent magnet material at a low permeancecoefficient and of the winding core operated close to saturation,electromagnetic propulsive efficiencies of a system like that describedhere can be brought well above 80% and even well above 90%, dependentstrongly on system requirements such as the thrust/lift ratio.

While a propulsion system may bear no relationship to the levitatingsuspension system, it is advantageous to share the two subsystems in asingle magnetic assembly, as now described. Let the bottom surface ofthe suspending rail include a periodic vertical ripple along the tracklength, as drawn, e.g., with a wavelength of one-half meter and a peakamplitude of one centimeter with an average suspension gap of twocentimeters, thus allowing a one centimeter minimum clearance at theripple crests. (The ripple need not be smooth, but could consist of fineor coarse steps in track height, although coarse steps would generatemore vibration harmonics in a motor than would a smooth ripple.) Forcontrol purposes, subdivide the signals associated with the magneticactuation sections 1600 through 1607 into three functional groupings: acommon mode grouping, with equal signal weighting and equal actuation toall the sections, for control of vertical height; a differential modegrouping, for a progression from negative to positive signal weightingand a similar progression for proportioning of actuation, for control ofpitch; and a wave grouping, scaled to the ripple wavelength of thetrack, for generating traveling magnetic waves that engage the ripplesIn the track and generate propulsion. The wave grouping can divide thetrack wavelength by an integer, e.g., quarter wavelength for afour-phase propulsion system, though the electronics indicated in FIG.16 do not depend on a fixed or integer relationship between trackwavelength and motor section spacing. To produce forward propulsion, agiven magnet section is energized to reinforce the permanent field, andthus increase the magnetic attraction, when the magnetic gap to thetrack is closing, and conversely, the section is energized with thereverse polarity to buck the permanent field, and thus reduceattraction, when the gap is opening. Since the force vector from amagnet to the track tilts forward when the gap is closing and backwardwhen the gap is opening, a synchronized variation in magnetic force canemphasize the forward-tilting lift force vector or, with a polarityreversal, emphasize the backward-tilting lift force vector, resulting inthrust or braking. The AC variation in magnetic flux for a given motorsection can be synchronized to the slope of the effective magnetic gap Xto the track, based on a difference in inductive measurements comparingthe motor sections on either side of a given motor section, asillustrated at the bottom of FIG. 16. As mentioned above, an approachworking with all actuators simultaneously reduces gap data to timevarying spatial sine and cosine components, which are fed back to drivewindings with appropriate phase and amplitude for desired thrust orbraking.

The electronic schematic shown in the lower portion of FIG. 16illustrates how the three groupings work. Function block 1636, repeatedeight times for the index “i” running from 0 to 7, receives inducedvoltage sense signals Vsi at 1632, generates drive voltages Vdi at 1634,generates effective magnetic gap output signals Xi at 1640, and receivesinputs (Φtgti for flux servo control targets at 1638. The principles forproducing such control modules are found in the earlier embodimentdescriptions of this Specification, allowing for various combinations ofapproaches using current sensing and induced voltage sensing, as well asallowing for well known methods of auxiliary sensing such as the use ofHall effect devices. Block 1636 implements the “inner” fast control loopthat varies switching regulator output voltage to cause measuredmagnetic flux to track a target value of flux with minimal phase delay.The operation of this loop is interpreted, e.g., as described withreference to the circuit of FIG. 12, to generate a signal indicating theeffective magnetic gap X, which is an output of 1636 used as a sensevariable in the slower outer loops for levitating suspension,controlling average height and longitudinal tilt. Gap X is also used forsynchronization of propulsive magnetic waves. The connection betweenmotor sections 1600 through 1607 and 1636 is via drive winding wirepairs like 1628 from 1607, via sense winding pairs like 1626 from 1607,all communicating via 32-wire bus or cable 1630, which splits into two16-wire buses or cables for the eight wire pairs providing the eightsense inputs Vsi at 1632 and eight drive outputs Vdi at 1634. Below 1636in the diagram, eight-wide buses at 1642, 1644, 1686, a674, and 1658,and at bus connections 1646, 1662, 1676, 1680, and 1638, carry signalsfor the eight channels operating motor modules 1600 through 1607. Thecircuit modules drawn represent groupings of eight similar or identicalcircuits, one for each motor module. The three rows of modules below andto the right of 1636 represent feedback paths for the three groupings ofsensors, going from top to bottom, for differential mode, for commonmode, and for periodic wave grouping to generate thrust.

Examining first the differential mode or tilt-control outer feedbackloop, position information Xi from 1636 communicates via output 1640 onbus 1642 to input 1646 into summing module 1648, which produces a singlechannel or scalar output on 1650 representing a weighted sum of theeight inputs. The weighting factor for each input is the input indexminus the average of the set of eight indices, a factor whose values are−3.5, −2.5, −1.5, −0.5, 0.5, 1.5, 2.5, and 3.5, factors varying inproportion to the distance of a given module center from the center ofthe group of eight. The output on 1650 enters module 1652, labeled“PIDdiff” and generating the Proportional, Integral, Differentialtransfer function for closing the servo loop in its differential modefor tilt control. The output of 1652 via 1654 to module 1656, calledXdiff at 1656, generates a set of eight proportioned drive outputs withthe same eight relative weighting factors used in module 1648, theoutputs emerging via bus 1658 and connecting to an input of “SUM” module1660. The differential mode signal, summed with other signals on each ofthe eight output leads from 1660 via bus 1644, provides eight-wide input1638 to module 1636, this input setting the set of target magneticfluxes for the inner servo loop. Thus, a distribution of fluxes andmagnetic forces is produced that dynamically corrects errors inlevitating tilt.

The common mode levitation feedback path operates similarly to thedifferential mode path just described, but lacks the separate channelweighting factors. The Xi signals on bus 1642 communicate via input 1662with summing module 1664, whose scalar output on 1665 varies inproportion to the effective magnetic gap X averaged over index “i” forthe eight actuation modules. Unity difference amplifier 1666 accepts the1665 signal as an input with +1 weighting and subtracts from this atarget X, “Xtgt” on input wire 1668 and with −1 weighting as labeled.The difference or error-X signal from 1666 on 1670 connects tocommon-mode PIDcmd transfer function module 1672, whose operation iscomparable to differential mode module 1652. The resulting output oneight-wide bus 1674 is eight identical signals going into SUM module1660 to sum with comparable differential and propulsion wave signals foroutput bus 1644 back to 1636.

The propulsion wave feedback path takes the Xi signal on 1642 to input1676 into differencing module 1678, whose normal operating mode is give,on output line i, the difference between Xi+1 and Xi−1, i.e. anindication of the slope of effective magnetic gap X at module i asindicated by a signal difference between the adjacent modules fore andaft of module i. The exception not indicated in the labeling of 1678 isfor end modules, where the slope estimate is based on an extrapolationfrom one side only rather than both sides. One can, for example, look ata signal difference one period down the row from the end, or thenegative of a signal difference a half period down the row, to estimatethe slope at an end module. The slope signals emerge from 1678 on a busterminating at input 1680 to variable gain module 1682, where each inputAi from the bus at 1680 is multiplied by thrust coefficient B from input1684, generating the eight gain-controlled signals, Ai*B on 1686 to theinput of SUM module 1660. One polarity of gain produces a positivemagnetic thrust, while an opposite gain polarity produces negativethrust, resulting in regenerative magnetic braking. The three eight-widebus inputs to 1660 give a single eight-wide output on 1644 to providethe eight target fluxes for the eight inner-loop magnetic servo circuitscollectively controlled by the three outer-loop servos.

An alternative approach to actuator position sense and flux controlweightings, for the thrust/braking degree of freedom, was mentionedabove, namely, two sets of periodic sinusoidal and cosinusoidalweightings of position sense and flux control, extending over the entireset of control modules. A sinusoidal set of position weightings thendrives a cosinusoidal set of flux control weightings, and a cosinusoidalset of position weightings drives a negative sinusoidal set of fluxcontrol weightings (as the derivative of the sine is the cosine and thederivative of the cosine is the negative sine), so that waves of fieldstrength variation along the row of electromagnets are synchronized toslope variations in vertical height of the track in order to producefore and aft actuation forces for thrust and braking.

In addition to the phase-shifted weighted output signals for producingthrust and braking, electromagnetic power can be conserved if themagnetic flux of individual electromagnetic modules is not forced toremain constant, but instead is allowed to vary inversely as theeffective time varying gap (called X or Xeff throughout thisSpecification) for variations associated with track ripple. In effect,individual control modules should be operated to correct collectiveerrors in height and fore/aft pitch angle, but should not be operated tominimize flux variations tending to occur in individual modules, in theabsence of corrective application of AC coil power, due to track ripple.Thus, a two-phase controller generating waves in flux strength,traveling along a row of electromagnetic modules, can be caused togenerate in-phase waves in target flux that minimize correspondingin-phase waves of coil current (allowing the field to vary as it dependspassively on the interaction of permanent magnets and a time-varyingflux gap, as if the drive windings were absent or open-circuited), whilesimultaneously generating quadrature-phase waves in target flux togenerate desired thrust or braking forces. Alternatively, to minimizepower squandered on unnecessary compensation for traveling waves of fluxstrength caused by track ripple, individual electromagnet controlmodules can be cross-coupled with neighbors so that flux perturbationsof certain wavelengths do not cause either corrective current actuationor passively induced currents that would be impeded by electricalresistance and thus cause the kind of damping and energy loss associatedwith shorting the windings of permanent magnet motors. The action ofsuch cross-coupling must then be reconciled with control to produceintentional actively driven waves of magnetic field strength forgeneration of thrust and braking.

It is noted that the wavelength and amplitude of vertical track ripplemight be varied along the track length, e.g., to give a greater slopeamplitude in regions where large forces will be required foraccelerating and decelerating, rating near a stop, or for generatingextra thrust to climb grades in the track, or to give a lesser slopeamplitude in regions where less thrust or braking is required and wherepower losses are reduced by a reduction in track ripple slope. If thetrack is designed for variable ripple wavelength, then the controlsystem over thrust and braking must be capable of adapting its groupingsand weightings of control modules in order to adapt to changing trackripple wavelengths. Microprocessor control and DSP (Digital SignalProcessor) control components are appropriate tools for implementationof such adaptive control over multiple modules.

Finally, various examples from prior art, e.g., Morishita (U.S. Pat. No.5,477,788), teach a suspension system of springs and dampers to decouplethe considerable inertia of the car from the lesser inertia of thelevitation magnets. Control problems arise when individualelectromagnets are independently suspended. A simpler system attachesall the electromagnets lifting a car to a single rigid frame, which inturn is decoupled from the car by a spring suspension. A mechanicalsuspension allows the lifting magnetic modules more easily to followirregularities in the track, allowing the path of the car to becorrected more smoothly and slowly through the suspension. It isrecognized that the control system must prevent modules from “fighting”one another “trying” to achieve some unachievable motion, e.g., asprevented by coupling of the modules to a rigid frame. In the schemeillustrated and discussed with reference to FIG. 16, the control foreach individual magnet is not a full levitation system, but rather aforce-control or flux-control system, responsive to a sum of signalinputs from a group controller. The outputs from this controller aredesigned to operate on the allowed degrees of freedom of the system,e.g., vertical motion, pitch angle, and forward motion, without excitinguseless patterns of actuation. As described above, specific correctionis made to prevent individual modules from responding to theintentionally built-in track ripple with an energy-wasting actuationpattern to maintain constant flux with the varying gap. With asuspension system (not shown in FIG. 16), the control system describedherein gains the advantage of following track irregularities with lesscorrection power. Excursion limit components such as rollers or skids,known in the art, are incorporated in the instant invention, while amechanical suspension permits the levitation magnets to follow largertrack irregularities before the limit components come into play.

In the suspension and control systems described earlier, control ofmagnetic flux has been preferred to control of current in the innercontrol loop of a motion control servo, since actuation force is morelinearly related to flux (roughly as a square law of flux) than tocurrent (roughly as tile of a ratio of current to inductance). Controlof current, like control of flux, shares the advantage over voltagecontrol of generating low phase lag in the servo loop. In the case ofmultiple magnetic actuators controlling a lesser number of degrees offreedom of a car, and where corrective actuation of modules tocompensate for track ripple is undesired, a controller approach is tohave individual magnet modules cause current to track a target current,as opposed to causing flux to track a target flux. Magnetic fluxinformation is provided, e.g. from sense coils or Hall effect sensors,by the separate modules, but flux control is achieved at the level ofgroupings of actuators, rather than for individual actuators. At ahigher tier of the system, translational and rotational motion iscontrolled via control of-groupings of flux at in intermediate tier.Thus, a three tier control system controls current and measures flux atthe module level, controls patterns of flux and/or force at theintermediate level, and controls position and rotation at the highestlevel. Such a control system directly avoids wasteful current responsesto track ripple at the level of individual modules, whereas a two-tiersystem with flux control at the lower tier relies on correctivecompensation going from the group controller to the individual modules.

Servo for Automotive Valve System

The systems described for solenoid control with soft landing can beapplied to the control of automotive valves, resulting in the completeelimination of the cam shaft and mechanical valve lifters. With anautomotive valve, one needs quick acceleration and deceleration of thevalve, closure of the valve with a minimum of impact, and significantholding force for both open and closed positions. For tight servocontrol at closure, an advantageous solenoid configuration is normallyopen, held by spring bias, with mechanical valve closure taking place ata very small magnetic gap, where servo control is at its best precision.The nonlinear control systems of either FIG. 7 or FIG. 12 will bepreferable to the more approximate “economy” methods for the bettercontrol afforded. As provided with the FIG. 12 system, the servo willneed dynamic rebiasing under the rapidly changing load conditionsassociated with changing engine speed and power, and the associatedaccelerations and dynamic gas flow pressures acting on the valve. Avalve may, under dynamically changing conditions, fall initiallyslightly short of closure or impact slightly, without damage, as long assmall errors are detected and corrected in subsequent operations withoutallowing operating errors to become large. The magnet core shouldsupport high flux for a high acceleration capability, as required athigh engine RPMs, indicating a metal core, either powder or finelaminations (or metal tape), as opposed to ferrites. For efficientcruising at moderate speeds, an engine control computer may idle one ormore individual cylinders by cutting off fuel intake and holding theexhaust valve continuously open, allowing the idled cylinder to breathewith no compression, by analogy to the operation of early gasolineengines lacking a throttle and operating by pulses of full poweralternating with multiple idling revolutions with an open exhaust valve.In the modem setting, operating cylinders will be subject to continuouspower control by fuel while other cylinders can remain idled untilneeded to meet an increased power demand.

1. A pump arrangement comprising: a) a selectively removable cassettecomprising: a housing a movable member associated with said housing in amanner to define a variable volume chamber; an inlet valve disposed insaid housing so as to selectively permit fluid to flow into the chamber;an outlet valve disposed in said housing so as to selectively permitfluid to flow out of the chamber; b) a solenoid which is separate fromsaid cassette and operatively connected with said movable member thatactuates the movable member in a manner to sequentially induct fluidinto and discharge fluid from the variabale volume chamber the solenoidincluding an armature; and c) a servo control system that senses theposition of the armature and determines, based on the sensed armatureposition, the volume of a fluid being pumped through the variable volumechamber.
 2. A pump as claimed in claim 1, wherein inlet valve and saidoutlet valve are respectively controlled by an inlet control solenoidand a discharge control solenoid.
 3. A pump as claimed in claim 1,wherein the movable member is a diaphragm.
 4. A pump as claimed in claim1, the servo control system further configured to detect, based upon thesensed armature position, the presence of gaseous bubbles within thefluid; and to determine the composition of the fluid based upon theresults of detecting the presence of gaseous bubbles within the fluid.5. The pump as claimed in claim 4, the servo control system furtherconfigured to: detect a first effective magnetic gap for said solenoidat a first magnetic force; alter the solenoid current to create a secondmagnetic force; detect a second effective magnetic gap for said solenoidresulting from the second magnetic force; calculate the change inmagnetic force; calculate the change between the first effectivemagnetic gap and the second magnetic gap; and calculate the complianceof the moveable member and the fluid within the variable volume chamberbased upon the change in magnetic force and the change between the firsteffective magnetic gap and the second magnetic gap.
 6. The pump asclaimed in claim 4, the servo control system further configured to:determine a frequency transient oscillation resulting from an impact ofa portion of said solenoid with the variable volume chamber; anddetermine the composition of the fluid based upon the frequencytransient oscillation.
 7. A pump arrangement comprising: a) aselectively removable cassette comprising: a housing a movable memberassociated with said housing in manner to define a variable volumechamber; an inlet valve disposed in said housing so as to selectivelypermit fluid to flow into the chamber; an outlet valve disposed in saidhousing so as to selectively permit fluid to flow out of the chamber,and b) a solenoid which is separate from said cassette and operativelyconnected with said movable member for actuating the movable member in amanner to sequentially induct fluid into and discharge fluid from thevariable volume chamber;  said solenoid comprising an armature; meansfor sensing the position of the armature; and means for determining,based on the sensed armature position, the composition of a fluid beingpumped through the variable volume chamber.
 8. A pump arrangementcomprising: a) a selectively removable cassette comprising: a housing amovable member associated with said housing in a manner to define avariable volume chamber; an inlet valve disposed in said housing so asto selectively permit fluid to flow into the chamber; an outlet valvedisposed in said housing so as to selectively permit fluid to flow outof the chamber, and b) a solenoid which is separate from said cassetteand operatively connected with said movable member that actuates themovable member in a manner to sequentially induct fluid into anddischarge fluid from the variable volume chamber;  said solenoidincluding an armature which is supported within a housing by a flatspring member which comprises: an outer member, an inner member; and twocurved connection portions which extend in first and second essentiallyopposed directions and which are each connected with the outer member atone end and with the inner member at the other.
 9. A pump arrangementcomprising: a) a selectively removable cassette comprising: a housing amovable member associated with said housing in a manner to define avariable volume chamber; an inlet valve disposed in said housing so asto selectively permit fluid to flow into the chamber; an outlet valvedisposed in said housing so as to selectively permit fluid to flow outof the chamber, and b) a solenoid which is separate from said cassetteand operatively connected with said movable member that actuates themovable member in a manner to sequentially induct fluid into anddischarge fluid from the variable volume chamber;  said solenoid havingan armature which is supported within a housing by first and second flatspring members, the first flat spring being connected to the armatureproximate a first end thereof and the second flat spring member beingconnected to the armature proximate a second end thereof, the first andsecond flat springs being operative to guide the armature so that itreciprocates back and forth along a predetermined axis, each of saidfirst and second flat springs comprising: an outer member; an innermember; and two curved connection portions which extend in first andsecond essentially opposed directions and which are each connected withthe outer member at one end and with the inner member at the other.